diff --git a/src/highlight.cpp b/src/highlight.cpp
index cc69010ec..91ef533c2 100644
--- a/src/highlight.cpp
+++ b/src/highlight.cpp
@@ -1033,7 +1033,7 @@ const highlighter_t::color_array_t &highlighter_t::highlight() {
             case symbol_if_clause:
             case symbol_else_clause:
             case symbol_case_item:
-            case symbol_boolean_statement:
+            case symbol_not_statement:
             case symbol_decorated_statement:
             case symbol_if_statement: {
                 this->color_children(node, parse_token_type_string, highlight_spec_command);
diff --git a/src/parse_constants.h b/src/parse_constants.h
index ef66ec9b1..b4f679b6a 100644
--- a/src/parse_constants.h
+++ b/src/parse_constants.h
@@ -19,6 +19,7 @@ enum parse_token_type_t {
     symbol_job_list,
     symbol_job_conjunction,
     symbol_job_conjunction_continuation,
+    symbol_job_decorator,
     symbol_job,
     symbol_job_continuation,
     symbol_statement,
@@ -35,7 +36,7 @@ enum parse_token_type_t {
     symbol_switch_statement,
     symbol_case_item_list,
     symbol_case_item,
-    symbol_boolean_statement,
+    symbol_not_statement,
     symbol_decorated_statement,
     symbol_plain_statement,
     symbol_arguments_or_redirections_list,
@@ -84,36 +85,9 @@ const enum_map<parse_token_type_t> token_enum_map[] = {
     {parse_token_type_andand, L"parse_token_type_andand"},
     {parse_token_type_oror, L"parse_token_type_oror"},
     {parse_token_type_terminate, L"parse_token_type_terminate"},
-    {symbol_andor_job_list, L"symbol_andor_job_list"},
-    {symbol_argument, L"symbol_argument"},
-    {symbol_argument_list, L"symbol_argument_list"},
-    {symbol_arguments_or_redirections_list, L"symbol_arguments_or_redirections_list"},
-    {symbol_begin_header, L"symbol_begin_header"},
-    {symbol_block_header, L"symbol_block_header"},
-    {symbol_block_statement, L"symbol_block_statement"},
-    {symbol_boolean_statement, L"symbol_boolean_statement"},
-    {symbol_case_item, L"symbol_case_item"},
-    {symbol_case_item_list, L"symbol_case_item_list"},
-    {symbol_decorated_statement, L"symbol_decorated_statement"},
-    {symbol_else_clause, L"symbol_else_clause"},
-    {symbol_else_continuation, L"symbol_else_continuation"},
-    {symbol_end_command, L"symbol_end_command"},
-    {symbol_for_header, L"symbol_for_header"},
-    {symbol_freestanding_argument_list, L"symbol_freestanding_argument_list"},
-    {symbol_function_header, L"symbol_function_header"},
-    {symbol_if_clause, L"symbol_if_clause"},
-    {symbol_if_statement, L"symbol_if_statement"},
-    {symbol_job, L"symbol_job"},
-    {symbol_job_conjunction, L"symbol_job_conjunction"},
-    {symbol_job_continuation, L"symbol_job_continuation"},
-    {symbol_job_list, L"symbol_job_list"},
-    {symbol_optional_newlines, L"symbol_optional_newlines"},
-    {symbol_optional_background, L"symbol_optional_background"},
-    {symbol_plain_statement, L"symbol_plain_statement"},
-    {symbol_redirection, L"symbol_redirection"},
-    {symbol_statement, L"symbol_statement"},
-    {symbol_switch_statement, L"symbol_switch_statement"},
-    {symbol_while_header, L"symbol_while_header"},
+// Define all symbols
+#define ELEM(sym) {symbol_##sym, L"symbol_" #sym},
+#include "parse_grammar_elements.inc"
     {token_type_invalid, L"token_type_invalid"},
     {token_type_invalid, NULL}};
 #define token_enum_map_len (sizeof token_enum_map / sizeof *token_enum_map)
@@ -165,7 +139,7 @@ enum parse_statement_decoration_t {
 };
 
 // Boolean statement types, stored in node tag.
-enum parse_bool_statement_type_t { parse_bool_and, parse_bool_or, parse_bool_not };
+enum parse_bool_statement_type_t { parse_bool_none, parse_bool_and, parse_bool_or };
 
 // Whether a statement is backgrounded.
 enum parse_optional_background_t { parse_no_background, parse_background };
diff --git a/src/parse_execution.cpp b/src/parse_execution.cpp
index 06f31a624..a54f6fb49 100644
--- a/src/parse_execution.cpp
+++ b/src/parse_execution.cpp
@@ -107,7 +107,7 @@ tnode_t<g::plain_statement> parse_execution_context_t::infinite_recursive_statem
     const wcstring &forbidden_function_name = parser->forbidden_function.back();
 
     // Get the first job in the job list.
-    tnode_t<g::job> first_job = job_list.try_get_child<g::job_conjunction, 0>().child<0>();
+    tnode_t<g::job> first_job = job_list.try_get_child<g::job_conjunction, 1>().child<0>();
     if (!first_job) {
         return {};
     }
@@ -215,7 +215,7 @@ bool parse_execution_context_t::job_is_simple_block(tnode_t<g::job> job_node) co
             return is_empty(statement.require_get_child<g::switch_statement, 0>().child<5>());
         case symbol_if_statement:
             return is_empty(statement.require_get_child<g::if_statement, 0>().child<3>());
-        case symbol_boolean_statement:
+        case symbol_not_statement:
         case symbol_decorated_statement:
             // not block statements
             return false;
@@ -921,33 +921,10 @@ bool parse_execution_context_t::determine_io_chain(tnode_t<g::arguments_or_redir
     return !errored;
 }
 
-parse_execution_result_t parse_execution_context_t::populate_boolean_process(
-    job_t *job, process_t *proc, tnode_t<g::boolean_statement> bool_statement) {
-    // Handle a boolean statement.
-    bool skip_job = false;
-    switch (bool_statement_type(bool_statement)) {
-        case parse_bool_and: {
-            // AND. Skip if the last job failed.
-            skip_job = (proc_get_last_status() != 0);
-            break;
-        }
-        case parse_bool_or: {
-            // OR. Skip if the last job succeeded.
-            skip_job = (proc_get_last_status() == 0);
-            break;
-        }
-        case parse_bool_not: {
-            // NOT. Negate it.
-            job->set_flag(JOB_NEGATE, !job->get_flag(JOB_NEGATE));
-            break;
-        }
-    }
-
-    if (skip_job) {
-        return parse_execution_skipped;
-    }
-    return this->populate_job_process(job, proc,
-                                      bool_statement.require_get_child<g::statement, 1>());
+parse_execution_result_t parse_execution_context_t::populate_not_process(
+    job_t *job, process_t *proc, tnode_t<g::not_statement> not_statement) {
+    job->set_flag(JOB_NEGATE, !job->get_flag(JOB_NEGATE));
+    return this->populate_job_process(job, proc, not_statement.child<1>());
 }
 
 template <typename Type>
@@ -985,8 +962,8 @@ parse_execution_result_t parse_execution_context_t::populate_job_process(
     parse_execution_result_t result = parse_execution_success;
 
     switch (specific_statement.type) {
-        case symbol_boolean_statement: {
-            result = this->populate_boolean_process(job, proc, {&tree(), &specific_statement});
+        case symbol_not_statement: {
+            result = this->populate_not_process(job, proc, {&tree(), &specific_statement});
             break;
         }
         case symbol_block_statement:
@@ -1224,6 +1201,7 @@ parse_execution_result_t parse_execution_context_t::run_job_conjunction(
     tnode_t<grammar::job_conjunction> job_expr, const block_t *associated_block) {
     parse_execution_result_t result = parse_execution_success;
     tnode_t<g::job_conjunction> cursor = job_expr;
+    // continuation is the parent of the cursor
     tnode_t<g::job_conjunction_continuation> continuation;
     while (cursor) {
         if (should_cancel_execution(associated_block)) break;
@@ -1232,13 +1210,7 @@ parse_execution_result_t parse_execution_context_t::run_job_conjunction(
             // Check the conjunction type.
             parse_bool_statement_type_t conj = bool_statement_type(continuation);
             assert((conj == parse_bool_and || conj == parse_bool_or) && "Unexpected conjunction");
-            if (conj == parse_bool_and) {
-                // Skip if last job failed.
-                skip = (proc_get_last_status() != 0);
-            } else if (conj == parse_bool_or) {
-                // Skip if last job succeeded.
-                skip = (proc_get_last_status() == 0);
-            }
+            skip = should_skip(conj);
         }
         if (! skip) {
             result = run_1_job(cursor.child<0>(), associated_block);
@@ -1249,20 +1221,40 @@ parse_execution_result_t parse_execution_context_t::run_job_conjunction(
     return result;
 }
 
+bool parse_execution_context_t::should_skip(parse_bool_statement_type_t type) const {
+    switch (type) {
+        case parse_bool_and:
+            // AND. Skip if the last job failed.
+            return proc_get_last_status() != 0;
+        case parse_bool_or:
+            // OR. Skip if the last job succeeded.
+            return proc_get_last_status() == 0;
+        default:
+            return false;
+    }
+}
+
 template <typename Type>
 parse_execution_result_t parse_execution_context_t::run_job_list(tnode_t<Type> job_list,
                                                                  const block_t *associated_block) {
+    // We handle both job_list and andor_job_list uniformly.
     static_assert(Type::token == symbol_job_list || Type::token == symbol_andor_job_list,
                   "Not a job list");
 
     parse_execution_result_t result = parse_execution_success;
-    while (tnode_t<g::job_conjunction> job_expr =
-               job_list.template next_in_list<g::job_conjunction>()) {
+    while (auto job_conj = job_list.template next_in_list<g::job_conjunction>()) {
         if (should_cancel_execution(associated_block)) break;
-        result = this->run_job_conjunction(job_expr, associated_block);
+
+        // Maybe skip the job if it has a leading and/or.
+        // Skipping is treated as success.
+        if (should_skip(get_decorator(job_conj))) {
+            result = parse_execution_success;
+        } else {
+            result = this->run_job_conjunction(job_conj, associated_block);
+        }
     }
 
-    // Returns the last job executed.
+    // Returns the result of the last job executed or skipped.
     return result;
 }
 
diff --git a/src/parse_execution.h b/src/parse_execution.h
index d15e69469..dceb87235 100644
--- a/src/parse_execution.h
+++ b/src/parse_execution.h
@@ -72,6 +72,9 @@ class parse_execution_context_t {
         tnode_t<grammar::job_list> job_list, wcstring *out_func_name) const;
     bool is_function_context() const;
 
+    /// Return whether we should skip a job with the given bool statement type.
+    bool should_skip(parse_bool_statement_type_t type) const;
+
     /// Indicates whether a job is a simple block (one block, no redirections).
     bool job_is_simple_block(tnode_t<grammar::job> job) const;
 
@@ -81,8 +84,8 @@ class parse_execution_context_t {
     // These create process_t structures from statements.
     parse_execution_result_t populate_job_process(job_t *job, process_t *proc,
                                                   tnode_t<grammar::statement> statement);
-    parse_execution_result_t populate_boolean_process(
-        job_t *job, process_t *proc, tnode_t<grammar::boolean_statement> bool_statement);
+    parse_execution_result_t populate_not_process(job_t *job, process_t *proc,
+                                                  tnode_t<grammar::not_statement> not_statement);
     parse_execution_result_t populate_plain_process(job_t *job, process_t *proc,
                                                     tnode_t<grammar::plain_statement> statement);
 
diff --git a/src/parse_grammar.h b/src/parse_grammar.h
index 99b021f4a..e08ccb62d 100644
--- a/src/parse_grammar.h
+++ b/src/parse_grammar.h
@@ -199,12 +199,20 @@ struct alternative {};
 
 // A job_list is a list of job_conjunctions, separated by semicolons or newlines
 DEF_ALT(job_list) {
-    using normal = seq<job_conjunction, job_list>;
+    using normal = seq<job_decorator, job_conjunction, job_list>;
     using empty_line = seq<tok_end, job_list>;
     using empty = grammar::empty;
     ALT_BODY(job_list, normal, empty_line, empty);
 };
 
+// Job decorators are 'and' and 'or'. These apply to the whole job.
+DEF_ALT(job_decorator) {
+    using ands = single<keyword<parse_keyword_and>>;
+    using ors = single<keyword<parse_keyword_or>>;
+    using empty = grammar::empty;
+    ALT_BODY(job_decorator, ands, ors, empty);
+};
+
 // A job_conjunction is a job followed by a continuation.
 DEF(job_conjunction) produces_sequence<job, job_conjunction_continuation> {
     BODY(job_conjunction);
@@ -231,12 +239,12 @@ DEF_ALT(job_continuation) {
 
 // A statement is a normal command, or an if / while / and etc
 DEF_ALT(statement) {
-    using boolean = single<boolean_statement>;
+    using nots = single<not_statement>;
     using block = single<block_statement>;
     using ifs = single<if_statement>;
     using switchs = single<switch_statement>;
     using decorated = single<decorated_statement>;
-    ALT_BODY(statement, boolean, block, ifs, switchs, decorated);
+    ALT_BODY(statement, nots, block, ifs, switchs, decorated);
 };
 
 // A block is a conditional, loop, or begin/end
@@ -304,19 +312,15 @@ DEF(function_header)
 produces_sequence<keyword<parse_keyword_function>, argument, argument_list, tok_end>{
     BODY(function_header)};
 
-//  A boolean statement is AND or OR or NOT
-DEF_ALT(boolean_statement) {
-    using ands = seq<keyword<parse_keyword_and>, statement>;  // foo ; and bar
-    using ors = seq<keyword<parse_keyword_or>, statement>;    // foo ; or bar
-    using nots = seq<keyword<parse_keyword_not>, statement>;  // not foo
-    ALT_BODY(boolean_statement, ands, ors, nots);
+DEF(not_statement) produces_sequence<keyword<parse_keyword_not>, statement> {
+    BODY(not_statement);
 };
 
 // An andor_job_list is zero or more job lists, where each starts with an `and` or `or` boolean
 // statement.
 DEF_ALT(andor_job_list) {
     using empty = grammar::empty;
-    using andor_job = seq<job_conjunction, andor_job_list>;
+    using andor_job = seq<job_decorator, job_conjunction, andor_job_list>;
     using empty_line = seq<tok_end, andor_job_list>;
     ALT_BODY(andor_job_list, empty, andor_job, empty_line);
 };
diff --git a/src/parse_grammar_elements.inc b/src/parse_grammar_elements.inc
index 1543a2a93..79339b6cb 100644
--- a/src/parse_grammar_elements.inc
+++ b/src/parse_grammar_elements.inc
@@ -1,6 +1,7 @@
 // Define ELEM before including this file.
 ELEM(job_list)
 ELEM(job)
+ELEM(job_decorator)
 ELEM(job_conjunction)
 ELEM(job_conjunction_continuation)
 ELEM(job_continuation)
@@ -18,7 +19,7 @@ ELEM(for_header)
 ELEM(while_header)
 ELEM(begin_header)
 ELEM(function_header)
-ELEM(boolean_statement)
+ELEM(not_statement)
 ELEM(andor_job_list)
 ELEM(decorated_statement)
 ELEM(plain_statement)
diff --git a/src/parse_productions.cpp b/src/parse_productions.cpp
index 94c56a38b..a09e28e13 100644
--- a/src/parse_productions.cpp
+++ b/src/parse_productions.cpp
@@ -61,6 +61,26 @@ RESOLVE(job_list) {
     }
 }
 
+// A job decorator is AND or OR
+RESOLVE(job_decorator) {
+    UNUSED(token2);
+
+    switch (token1.keyword) {
+        case parse_keyword_and: {
+            *out_tag = parse_bool_and;
+            return production_for<ands>();
+        }
+        case parse_keyword_or: {
+            *out_tag = parse_bool_or;
+            return production_for<ors>();
+        }
+        default: {
+            *out_tag = parse_bool_none;
+            return production_for<empty>();
+        }
+    }
+}
+
 RESOLVE(job_conjunction_continuation) {
     UNUSED(token2);
     UNUSED(out_tag);
@@ -123,10 +143,8 @@ RESOLVE(statement) {
     switch (token1.type) {
         case parse_token_type_string: {
             switch (token1.keyword) {
-                case parse_keyword_and:
-                case parse_keyword_or:
                 case parse_keyword_not: {
-                    return production_for<boolean>();
+                    return production_for<nots>();
                 }
                 case parse_keyword_for:
                 case parse_keyword_while:
@@ -260,27 +278,6 @@ RESOLVE(block_header) {
     }
 }
 
-// A boolean statement is AND or OR or NOT.
-RESOLVE(boolean_statement) {
-    UNUSED(token2);
-
-    switch (token1.keyword) {
-        case parse_keyword_and: {
-            *out_tag = parse_bool_and;
-            return production_for<ands>();
-        }
-        case parse_keyword_or: {
-            *out_tag = parse_bool_or;
-            return production_for<ors>();
-        }
-        case parse_keyword_not: {
-            *out_tag = parse_bool_not;
-            return production_for<nots>();
-        }
-        default: { return NO_PRODUCTION; }
-    }
-}
-
 RESOLVE(decorated_statement) {
 
     // If this is e.g. 'command --help' then the command is 'command' and not a decoration. If the
diff --git a/src/parse_util.cpp b/src/parse_util.cpp
index 83860912a..2927763ee 100644
--- a/src/parse_util.cpp
+++ b/src/parse_util.cpp
@@ -1072,17 +1072,15 @@ static bool detect_errors_in_backgrounded_job(tnode_t<grammar::job> job,
                "Expected first job to be the node we found");
         (void)first_jconj;
 
-        // Try getting the next job as a boolean statement.
-        tnode_t<g::job> next_job = jlist.next_in_list<g::job_conjunction>().child<0>();
-        tnode_t<g::statement> next_stmt = next_job.child<0>();
-        if (auto bool_stmt = next_stmt.try_get_child<g::boolean_statement, 0>()) {
+        // Try getting the next job's decorator.
+        if (auto next_job_dec = jlist.next_in_list<g::job_decorator>()) {
             // The next job is indeed a boolean statement.
-            parse_bool_statement_type_t bool_type = bool_statement_type(bool_stmt);
-            if (bool_type == parse_bool_and) {  // this is not allowed
-                errored = append_syntax_error(parse_errors, bool_stmt.source_range()->start,
+            parse_bool_statement_type_t bool_type = bool_statement_type(next_job_dec);
+            if (bool_type == parse_bool_and) {
+                errored = append_syntax_error(parse_errors, next_job_dec.source_range()->start,
                                               BOOL_AFTER_BACKGROUND_ERROR_MSG, L"and");
-            } else if (bool_type == parse_bool_or) {  // this is not allowed
-                errored = append_syntax_error(parse_errors, bool_stmt.source_range()->start,
+            } else if (bool_type == parse_bool_or) {
+                errored = append_syntax_error(parse_errors, next_job_dec.source_range()->start,
                                               BOOL_AFTER_BACKGROUND_ERROR_MSG, L"or");
             }
         }
@@ -1100,7 +1098,8 @@ static bool detect_errors_in_plain_statement(const wcstring &buff_src,
 
     // In a few places below, we want to know if we are in a pipeline.
     tnode_t<statement> st = pst.try_get_parent<decorated_statement>().try_get_parent<statement>();
-    const bool is_in_pipeline = statement_is_in_pipeline(st, true /* count first */);
+    pipeline_position_t pipe_pos = get_pipeline_position(st);
+    bool is_in_pipeline = (pipe_pos != pipeline_position_t::none);
 
     // We need to know the decoration.
     const enum parse_statement_decoration_t decoration = get_decoration(pst);
@@ -1110,6 +1109,19 @@ static bool detect_errors_in_plain_statement(const wcstring &buff_src,
         errored = append_syntax_error(parse_errors, source_start, EXEC_ERR_MSG, L"exec");
     }
 
+    // This is a somewhat stale check that 'and' and 'or' are not in pipelines, except at the
+    // beginning. We can't disallow them as commands entirely because we need to support 'and
+    // --help', etc.
+    if (pipe_pos == pipeline_position_t::subsequent) {
+        // check if our command is 'and' or 'or'. This is very clumsy; we don't catch e.g. quoted
+        // commands.
+        wcstring command = pst.child<0>().get_source(buff_src);
+        if (command == L"and" || command == L"or") {
+            errored =
+                append_syntax_error(parse_errors, source_start, EXEC_ERR_MSG, command.c_str());
+        }
+    }
+
     if (maybe_t<wcstring> mcommand = command_for_plain_statement(pst, buff_src)) {
         wcstring command = std::move(*mcommand);
         // Check that we can expand the command.
@@ -1254,16 +1266,9 @@ parser_test_error_bits_t parse_util_detect_errors(const wcstring &buff_src,
                 has_unclosed_block = true;
             } else if (node.type == symbol_statement && !node.has_source()) {
                 // Check for a statement without source in a pipeline, i.e. unterminated pipeline.
-                has_unclosed_pipe |= statement_is_in_pipeline({&node_tree, &node}, false);
-            } else if (node.type == symbol_boolean_statement) {
-                // 'or' and 'and' can be in a pipeline, as long as they're first.
-                tnode_t<g::boolean_statement> gbs{&node_tree, &node};
-                parse_bool_statement_type_t type = bool_statement_type(gbs);
-                if ((type == parse_bool_and || type == parse_bool_or) &&
-                    statement_is_in_pipeline(gbs.try_get_parent<g::statement>(),
-                                             false /* don't count first */)) {
-                    errored = append_syntax_error(&parse_errors, node.source_start, EXEC_ERR_MSG,
-                                                  (type == parse_bool_and) ? L"and" : L"or");
+                auto pipe_pos = get_pipeline_position({&node_tree, &node});
+                if (pipe_pos != pipeline_position_t::none) {
+                    has_unclosed_pipe = true;
                 }
             } else if (node.type == symbol_argument) {
                 tnode_t<g::argument> arg{&node_tree, &node};
diff --git a/src/tnode.cpp b/src/tnode.cpp
index 64b93d124..8e4a447fb 100644
--- a/src/tnode.cpp
+++ b/src/tnode.cpp
@@ -46,7 +46,7 @@ enum parse_statement_decoration_t get_decoration(tnode_t<grammar::plain_statemen
     return decoration;
 }
 
-enum parse_bool_statement_type_t bool_statement_type(tnode_t<grammar::boolean_statement> stmt) {
+enum parse_bool_statement_type_t bool_statement_type(tnode_t<grammar::job_decorator> stmt) {
     return static_cast<parse_bool_statement_type_t>(stmt.tag());
 }
 
@@ -111,24 +111,35 @@ bool job_node_is_background(tnode_t<grammar::job> job) {
     return bg.tag() == parse_background;
 }
 
-bool statement_is_in_pipeline(tnode_t<grammar::statement> st, bool include_first) {
+parse_bool_statement_type_t get_decorator(tnode_t<grammar::job_conjunction> conj) {
+    using namespace grammar;
+    tnode_t<job_decorator> dec;
+    // We have two possible parents: job_list and andor_job_list.
+    if (auto p = conj.try_get_parent<job_list>()) {
+        dec = p.require_get_child<job_decorator, 0>();
+    } else if (auto p = conj.try_get_parent<andor_job_list>()) {
+        dec = p.require_get_child<job_decorator, 0>();
+    }
+    // note this returns 0 (none) if dec is empty.
+    return bool_statement_type(dec);
+}
+
+pipeline_position_t get_pipeline_position(tnode_t<grammar::statement> st) {
     using namespace grammar;
     if (!st) {
-        return false;
+        return pipeline_position_t::none;
     }
 
     // If we're part of a job continuation, we're definitely in a pipeline.
     if (st.try_get_parent<job_continuation>()) {
-        return true;
+        return pipeline_position_t::subsequent;
     }
 
-    // If include_first is set, check if we're the beginning of a job, and if so, whether that job
+    // Check if we're the beginning of a job, and if so, whether that job
     // has a non-empty continuation.
-    if (include_first) {
-        tnode_t<job_continuation> jc = st.try_get_parent<job>().child<1>();
-        if (jc.try_get_child<statement, 2>()) {
-            return true;
-        }
+    tnode_t<job_continuation> jc = st.try_get_parent<job>().child<1>();
+    if (jc.try_get_child<statement, 2>()) {
+        return pipeline_position_t::first;
     }
-    return false;
+    return pipeline_position_t::none;
 }
diff --git a/src/tnode.h b/src/tnode.h
index 92fde8da4..60fac38b6 100644
--- a/src/tnode.h
+++ b/src/tnode.h
@@ -234,7 +234,7 @@ maybe_t<wcstring> command_for_plain_statement(tnode_t<grammar::plain_statement>
 parse_statement_decoration_t get_decoration(tnode_t<grammar::plain_statement> stmt);
 
 /// Return the type for a boolean statement.
-enum parse_bool_statement_type_t bool_statement_type(tnode_t<grammar::boolean_statement> stmt);
+enum parse_bool_statement_type_t bool_statement_type(tnode_t<grammar::job_decorator> stmt);
 
 enum parse_bool_statement_type_t bool_statement_type(tnode_t<grammar::job_conjunction_continuation> stmt);
 
@@ -253,9 +253,19 @@ arguments_node_list_t get_argument_nodes(tnode_t<grammar::arguments_or_redirecti
 /// Return whether the given job is background because it has a & symbol.
 bool job_node_is_background(tnode_t<grammar::job>);
 
-/// Return whether the statement is part of a pipeline. If include_first is set, the first command
-/// in a pipeline is considered part of it; otherwise only the second or additional commands are.
-bool statement_is_in_pipeline(tnode_t<grammar::statement> st, bool include_first);
+/// If the conjunction is has a decorator (and/or), return it; otherwise return none. This only
+/// considers the leading conjunction, e.g. in `and true || false` only the 'true' conjunction will
+/// return 'and'.
+parse_bool_statement_type_t get_decorator(tnode_t<grammar::job_conjunction>);
+
+/// Return whether the statement is part of a pipeline.
+/// This doesn't detect e.g. pipelines involving our parent's block statements.
+enum class pipeline_position_t {
+    none,       // not part of a pipeline
+    first,      // first command in a pipeline
+    subsequent  // second or further command in a pipeline
+};
+pipeline_position_t get_pipeline_position(tnode_t<grammar::statement> st);
 
 /// Check whether an argument_list is a root list.
 inline bool argument_list_is_root(tnode_t<grammar::argument_list> list) {
diff --git a/tests/andandoror.in b/tests/andandoror.in
index f2093039b..f739cc1ea 100644
--- a/tests/andandoror.in
+++ b/tests/andandoror.in
@@ -20,7 +20,7 @@ set beta 0
 set gamma 0
 set delta 0
 while [ $alpha -lt 2 ] && [ $beta -lt 3 ]
-      and [ $gamma -lt 4 ] || [ $delta -lt 5 ]
+      or [ $gamma -lt 4 ] || [ $delta -lt 5 ]
     echo $alpha $beta $gamma
     set alpha ( math $alpha + 1 )
     set beta ( math $beta + 1 )
@@ -31,3 +31,8 @@ end
 logmsg "Complex scenarios"
 
 begin; echo 1 ; false ; end || begin ; echo 2 && echo 3 ; end
+
+if false && true
+   or not false
+   echo 4
+end
diff --git a/tests/andandoror.out b/tests/andandoror.out
index e8f8f8bed..84f9f04f2 100644
--- a/tests/andandoror.out
+++ b/tests/andandoror.out
@@ -28,3 +28,4 @@ if test 4 ok
 1
 2
 3
+4