diff --git a/src/exec.cpp b/src/exec.cpp
index d451ed688..5d36f5ca9 100644
--- a/src/exec.cpp
+++ b/src/exec.cpp
@@ -983,7 +983,7 @@ bool exec_job(parser_t &parser, const shared_ptr<job_t> &j, const io_chain_t &bl
         // A false return tells the caller to remove the job from the list.
         return false;
     }
-    cleanup_t timer = push_timer(j->flags().has_time_prefix && !no_exec());
+    cleanup_t timer = push_timer(j->wants_timing() && !no_exec());
 
     // Get the deferred process, if any. We will have to remember its pipes.
     autoclose_pipes_t deferred_pipes;
diff --git a/src/parse_execution.cpp b/src/parse_execution.cpp
index 786e9948b..6d17c152d 100644
--- a/src/parse_execution.cpp
+++ b/src/parse_execution.cpp
@@ -998,12 +998,6 @@ end_execution_reason_t parse_execution_context_t::populate_not_process(
     job_t *job, process_t *proc, const ast::not_statement_t &not_statement) {
     auto &flags = job->mut_flags();
     flags.negate = !flags.negate;
-    if (not_statement.time) {
-        flags.has_time_prefix = true;
-        if (job->is_initially_background()) {
-            return this->report_error(STATUS_INVALID_ARGS, not_statement, ERROR_TIME_BACKGROUND);
-        }
-    }
     return this->populate_job_process(job, proc, not_statement.contents, not_statement.variables);
 }
 
@@ -1151,12 +1145,6 @@ end_execution_reason_t parse_execution_context_t::populate_job_from_job_node(
     // Create processes. Each one may fail.
     process_list_t processes;
     processes.emplace_back(new process_t());
-    if (job_node.time) {
-        j->mut_flags().has_time_prefix = true;
-        if (job_node.bg) {
-            return this->report_error(STATUS_INVALID_ARGS, job_node, ERROR_TIME_BACKGROUND);
-        }
-    }
     end_execution_reason_t result = this->populate_job_process(
         j, processes.back().get(), job_node.statement, job_node.variables);
 
@@ -1210,6 +1198,32 @@ static bool remove_job(parser_t &parser, job_t *job) {
     return false;
 }
 
+/// Decide if a job node should be 'time'd.
+/// For historical reasons the 'not' and 'time' prefix are "inside out". That is, it's
+/// 'not time cmd'. Note that a time appearing anywhere in the pipeline affects the whole job.
+/// `sleep 1 | not time true` will time the whole job!
+static bool job_node_wants_timing(const ast::job_t &job_node) {
+    // Does our job have the job-level time prefix?
+    if (job_node.time) return true;
+
+    // Helper to return true if a node is 'not time ...' or 'not not time...' or...
+    auto is_timed_not_statement = [](const ast::statement_t &stat) {
+        const auto *ns = stat.contents->try_as<ast::not_statement_t>();
+        while (ns) {
+            if (ns->time) return true;
+            ns = ns->contents.try_as<ast::not_statement_t>();
+        }
+        return false;
+    };
+
+    // Do we have a 'not time ...' anywhere in our pipeline?
+    if (is_timed_not_statement(job_node.statement)) return true;
+    for (const ast::job_continuation_t &jc : job_node.continuation) {
+        if (is_timed_not_statement(jc.statement)) return true;
+    }
+    return false;
+}
+
 end_execution_reason_t parse_execution_context_t::run_1_job(const ast::job_t &job_node,
                                                             const block_t *associated_block) {
     if (auto ret = check_end_execution()) {
@@ -1306,6 +1320,12 @@ end_execution_reason_t parse_execution_context_t::run_1_job(const ast::job_t &jo
         ld.is_subshell || ld.is_block || ld.is_event || !parser->is_interactive();
     props.from_event_handler = ld.is_event;
     props.job_control = wants_job_control;
+    props.wants_timing = job_node_wants_timing(job_node);
+
+    // It's an error to have 'time' in a background job.
+    if (props.wants_timing && props.initial_background) {
+        return this->report_error(STATUS_INVALID_ARGS, job_node, ERROR_TIME_BACKGROUND);
+    }
 
     shared_ptr<job_t> job = std::make_shared<job_t>(props, get_source(job_node));
 
diff --git a/src/proc.h b/src/proc.h
index cd6852fe8..73973cd04 100644
--- a/src/proc.h
+++ b/src/proc.h
@@ -318,6 +318,9 @@ class job_t {
         /// initial state should be.
         bool initial_background{};
 
+        /// Whether the job has the 'time' prefix and so we should print timing for this job.
+        bool wants_timing{};
+
         /// Whether this job was created as part of an event handler.
         bool from_event_handler{};
 
@@ -409,9 +412,6 @@ class job_t {
         /// This job is disowned, and should be removed from the active jobs list.
         bool disown_requested{false};
 
-        /// Whether to print timing for this job.
-        bool has_time_prefix{false};
-
         // Indicates that we are the "group root." Any other jobs using this tree are nested.
         bool is_group_root{false};
 
@@ -423,6 +423,9 @@ class job_t {
     /// Access mutable job flags.
     flags_t &mut_flags() { return job_flags; }
 
+    // \return whether we should print timing information.
+    bool wants_timing() const { return properties.wants_timing; }
+
     /// \return if we want job control.
     bool wants_job_control() const { return properties.job_control; }