diff --git a/ci/build-helpers.sh b/ci/build-helpers.sh
index 3069fd9f..6d5337f9 100755
--- a/ci/build-helpers.sh
+++ b/ci/build-helpers.sh
@@ -195,7 +195,13 @@ function short_timeout () { general_timeout "$TIMEOUT" "$@"; }
 function long_timeout () { general_timeout "$LONG_TIMEOUT" "$@"; }
 function general_timeout () {
   local ret=0 short_cmd
-  $timeout_exec -s9 "$@" || ret=$?
+  # Beware: backgrounding $timeout_exec means that it cannot read stdin!
+  $timeout_exec -s9 "$@" &
+  # `timeout` makes a new process group. If we're killed now, also kill it.
+  # shellcheck disable=SC2064   # expanding $! now is intentional
+  trap "kill $!; trap_handler" INT TERM
+  wait || ret=$?
+  trap trap_handler INT TERM    # reset traps once `timeout` has exited
   # 124 if command times out; 137 if command is killed (including by timeout itself)
   if [ $ret -eq 124 ] || [ $ret -eq 137 ]; then
     # BASH_{SOURCE,LINENO}[0] is where we're being called from, which is inside
@@ -212,3 +218,16 @@ function general_timeout () {
   fi
   return $ret
 }
+
+# Set this function to be invoked when killed using `trap trap_handler INT TERM`.
+# When killed, make sure we exit cleanly by killing all subshells and processes
+# in our process group. Long-running commands need special handling as commands
+# are invoked by bash in their own process group; see the general_timeout
+# function for details.
+function trap_handler () {
+  # Reset trap handler so we don't recurse forever when killing ourselves below.
+  trap - INT TERM
+  # Kill everything in our process group (i.e. subshells that bash spawned).
+  # This does *not* include subprocesses run by bash, only subshells.
+  kill -- -$$
+}
diff --git a/ci/build-loop.sh b/ci/build-loop.sh
index 3c15a5eb..3e5ea81f 100755
--- a/ci/build-loop.sh
+++ b/ci/build-loop.sh
@@ -41,7 +41,7 @@ echo "$HASHES" | tail -n "+$((BUILD_SEQ + 1))" | cat -n | while read -r ahead bt
       # API request quota too quickly.
       succeeded) ;;
     esac
-  ) < /dev/null  # Stop commands from slurping hashes, just in case.
+  ) & wait  # Stop commands from slurping hashes; make "trap" work.
 done
 
 case "$BUILD_TYPE" in
diff --git a/ci/continuous-builder.sh b/ci/continuous-builder.sh
index 5b5a07e8..4e074e1f 100755
--- a/ci/continuous-builder.sh
+++ b/ci/continuous-builder.sh
@@ -6,6 +6,10 @@
 
 . build-helpers.sh
 
+# Make sure we exit cleanly and don't leave leftover processes running when
+# killed. Bash doesn't do this automatically, unfortunately.
+trap trap_handler INT TERM
+
 if [ "$1" != --skip-setup ]; then
   if [ -r ~/.continuous-builder ]; then
     # Tell ShellCheck not to check the sourced file here. Assume the .env files are fine.
@@ -107,9 +111,12 @@ if [ -n "$HASHES" ]; then
       # Run the build
       . build-loop.sh
 
-      # Something inside this subshell is reading stdin, which causes some hashes
-      # from above to be ignored. It shouldn't, so redirect from /dev/null.
-    ) < /dev/null
+      # Something inside this subshell is reading stdin, which used to cause
+      # some hashes from above to be ignored. Let "&" redirect from /dev/null.
+      # Additionally, use "& wait" so that the trap set above can run properly.
+      # If we just ran the subshell normally, bash would wait for it to exit
+      # before invoking the trap handler, which would take too long.
+    ) & wait
 
     # Outside subshell; we're back in the parent directory.
     # Delete builds older than 2 days, then keep deleting until we've got at
@@ -161,7 +168,9 @@ run_duration=$(($(date +%s) - run_start_time))
 # shellcheck disable=SC2031  # TIMEOUT was modified in a subshell; that's fine.
 timeout=$(get_config_value timeout "${TIMEOUT:-120}")
 if [ "$run_duration" -lt "$timeout" ]; then
-  sleep $((timeout - run_duration)) || :
+  # Wrap this in short_timeout so that sleep gets killed properly when the outer
+  # script is killed.
+  TIMEOUT=$timeout short_timeout sleep $((timeout - run_duration))
 fi
 
 # Re-exec ourselves. This lets us update pick up updates to this script, e.g.