diff --git a/src/builtin_disown.cpp b/src/builtin_disown.cpp
index 3c9822df7..510044803 100644
--- a/src/builtin_disown.cpp
+++ b/src/builtin_disown.cpp
@@ -36,7 +36,7 @@ static int disown_job(const wchar_t *cmd, parser_t &parser, io_streams_t &stream
     // within the context of a subjob which will cause the parent job to crash in exec_job().
     // Instead, we set a flag and the parser removes the job from the jobs list later.
     j->mut_flags().disown_requested = true;
-    if (pgid) add_disowned_pgid(*pgid);
+    add_disowned_job(j);
 
     return STATUS_CMD_OK;
 }
diff --git a/src/proc.cpp b/src/proc.cpp
index f65651c38..9ab2ceb43 100644
--- a/src/proc.cpp
+++ b/src/proc.cpp
@@ -326,13 +326,24 @@ bool job_t::has_external_proc() const {
 /// we exit. Poll these from time-to-time to prevent zombie processes from happening (#5342).
 static owning_lock<std::vector<pid_t>> s_disowned_pids;
 
-void add_disowned_pgid(pid_t pgid) {
-    // NEVER add our own (or an invalid) pgid as they are not unique to only
+void add_disowned_job(job_t *j) {
+    if (j == nullptr) return;
+
+    // Never add our own (or an invalid) pgid as it is not unique to only
     // one job, and may result in a deadlock if we attempt the wait.
-    if (pgid != getpgrp() && pgid > 0) {
+    auto pgid = j->get_pgid();
+    auto disowned_pids = s_disowned_pids.acquire();
+    if (pgid && *pgid != getpgrp() && *pgid > 0) {
         // waitpid(2) is signalled to wait on a process group rather than a
         // process id by using the negative of its value.
-        s_disowned_pids.acquire()->push_back(pgid * -1);
+        disowned_pids->push_back(*pgid * -1);
+    } else {
+        // Instead, add the PIDs of any external processes
+        for (auto &process : j->processes) {
+            if (process->pid) {
+                disowned_pids->push_back(process->pid);
+            }
+        }
     }
 }
 
@@ -341,8 +352,14 @@ static void reap_disowned_pids() {
     auto disowned_pids = s_disowned_pids.acquire();
     auto try_reap1 = [](pid_t pid) {
         int status;
-        return waitpid(pid, &status, WNOHANG) > 0;
+        int ret = waitpid(pid, &status, WNOHANG);
+        if (ret > 0) {
+            FLOGF(proc_reap_external, "Reaped disowned PID or PGID %d", pid);
+        }
+        return ret;
     };
+    // waitpid returns 0 iff the PID/PGID in question has not changed state; remove the pid/pgid
+    // if it has changed or an error occurs (presumably ECHILD because the child does not exist)
     disowned_pids->erase(std::remove_if(disowned_pids->begin(), disowned_pids->end(), try_reap1),
                          disowned_pids->end());
 }
diff --git a/src/proc.h b/src/proc.h
index 934eab2b5..f9ce8d50b 100644
--- a/src/proc.h
+++ b/src/proc.h
@@ -551,9 +551,9 @@ void hup_jobs(const job_list_t &jobs);
 /// \return 1 if transferred, 0 if no transfer was necessary, -1 on error.
 int terminal_maybe_give_to_job_group(const job_group_t *jg, bool continuing_from_stopped);
 
-/// Add a pid to the list of pids we wait on even though they are not associated with any jobs.
-/// Used to avoid zombie processes after disown.
-void add_disowned_pgid(pid_t pgid);
+/// Add a job to the list of PIDs/PGIDs we wait on even though they are not associated with any
+/// jobs. Used to avoid zombie processes after disown.
+void add_disowned_job(job_t *j);
 
 bool have_proc_stat();
 
diff --git a/tests/checks/jobs.fish b/tests/checks/jobs.fish
index ed72e827d..1ad32670d 100644
--- a/tests/checks/jobs.fish
+++ b/tests/checks/jobs.fish
@@ -1,4 +1,19 @@
 #RUN: %fish %s
+
+# Verify zombies are not left by disown (#7183, #5342)
+# Do this first to avoid colliding with the other disowned processes below, which may
+# still be running at the end of the script
+sleep 0.2 &
+disown
+sleep 0.2
+echo Trigger process reaping
+#CHECK: Trigger process reaping
+# The initial approach here was to kill the PID of the sleep process, which should
+# be gone by the time we get here. Unfortunately, kill from procps on pre-2016 distributions
+# does not print an error for non-existent PIDs, so instead look for zombies in this session
+# (there should be none).
+ps -o state | string match 'Z*'
+
 jobs -q
 echo $status
 #CHECK: 1