diff --git a/Library/Homebrew/cmd/update.sh b/Library/Homebrew/cmd/update.sh
index 2bf3bb32722a2..4c0bc7c601867 100644
--- a/Library/Homebrew/cmd/update.sh
+++ b/Library/Homebrew/cmd/update.sh
@@ -1,11 +1,15 @@
 # Documentation defined in Library/Homebrew/cmd/update.rb
 
-# HOMEBREW_CURLRC, HOMEBREW_DEVELOPER, HOMEBREW_GIT_EMAIL, HOMEBREW_GIT_NAME
-# HOMEBREW_UPDATE_CLEANUP, HOMEBREW_UPDATE_TO_TAG are from the user environment
+# HOMEBREW_API_DOMAIN, HOMEBREW_CURLRC, HOMEBREW_DEBUG, HOMEBREW_DEVELOPER, HOMEBREW_GIT_EMAIL, HOMEBREW_GIT_NAME,
+# HOMEBREW_GITHUB_API_TOKEN, HOMEBREW_NO_ENV_HINTS, HOMEBREW_NO_INSTALL_CLEANUP, HOMEBREW_NO_INSTALL_FROM_API,
+# HOMEBREW_UPDATE_TO_TAG are from the user environment
 # HOMEBREW_LIBRARY, HOMEBREW_PREFIX, HOMEBREW_REPOSITORY are set by bin/brew
-# HOMEBREW_BREW_DEFAULT_GIT_REMOTE, HOMEBREW_BREW_GIT_REMOTE, HOMEBREW_CACHE, HOMEBREW_CELLAR, HOMEBREW_CURL
-# HOMEBREW_DEV_CMD_RUN, HOMEBREW_FORCE_BREWED_CURL, HOMEBREW_FORCE_BREWED_GIT, HOMEBREW_SYSTEM_CURL_TOO_OLD
-# HOMEBREW_USER_AGENT_CURL are set by brew.sh
+# HOMEBREW_API_DEFAULT_DOMAIN, HOMEBREW_AUTO_UPDATE_CASK_TAP, HOMEBREW_AUTO_UPDATE_CORE_TAP,
+# HOMEBREW_AUTO_UPDATE_SECS, HOMEBREW_BREW_DEFAULT_GIT_REMOTE, HOMEBREW_BREW_GIT_REMOTE, HOMEBREW_CACHE,
+# HOMEBREW_CASK_REPOSITORY, HOMEBREW_CELLAR, HOMEBREW_CORE_DEFAULT_GIT_REMOTE, HOMEBREW_CORE_GIT_REMOTE,
+# HOMEBREW_CORE_REPOSITORY, HOMEBREW_CURL, HOMEBREW_DEV_CMD_RUN, HOMEBREW_FORCE_BREWED_CA_CERTIFICATES,
+# HOMEBREW_FORCE_BREWED_CURL, HOMEBREW_FORCE_BREWED_GIT, HOMEBREW_LINUXBREW_CORE_MIGRATION,
+# HOMEBREW_SYSTEM_CURL_TOO_OLD, HOMEBREW_USER_AGENT_CURL are set by brew.sh
 # shellcheck disable=SC2154
 source "${HOMEBREW_LIBRARY}/Homebrew/utils/lock.sh"
 
@@ -369,9 +373,9 @@ EOS
     set -x
   fi
 
-  if [[ -z "${HOMEBREW_UPDATE_CLEANUP}" && -z "${HOMEBREW_UPDATE_TO_TAG}" ]]
+  if [[ -z "${HOMEBREW_UPDATE_TO_TAG}" ]]
   then
-    if [[ -n "${HOMEBREW_DEVELOPER}" || -n "${HOMEBREW_DEV_CMD_RUN}" ]]
+    if [[ -n "${HOMEBREW_DEVELOPER}" || -n "${HOMEBREW_DEV_CMD_RUN}" ]] && [[ -n "${HOMEBREW_NO_INSTALL_CLEANUP}" ]]
     then
       export HOMEBREW_NO_UPDATE_CLEANUP="1"
     else