diff --git a/Library/Homebrew/brew.sh b/Library/Homebrew/brew.sh
index 3345eb0da6..b1e1faa11b 100644
--- a/Library/Homebrew/brew.sh
+++ b/Library/Homebrew/brew.sh
@@ -230,7 +230,16 @@ EOS
 # exceeds 3 seconds.
 update-preinstall-timer() {
   sleep 3
-  echo 'Updating Homebrew...' >&2
+  # Outputting a command but don't want to run it, hence single quotes.
+  # shellcheck disable=SC2016
+  echo 'Running `brew update --preinstall`...' >&2
+  if [[ -z "${HOMEBREW_NO_ENV_HINTS}" && -z "${HOMEBREW_AUTO_UPDATE_SECS}" ]]
+  then
+    # shellcheck disable=SC2016
+    echo 'Adjust how often this is run with HOMEBREW_AUTO_UPDATE_SECS or disable with' >&2
+    # shellcheck disable=SC2016
+    echo 'HOMEBREW_NO_AUTO_UPDATE. Hide these hints with HOMEBREW_NO_ENV_HINTS (see `man brew`).' >&2
+  fi
 }
 
 # These variables are set from various Homebrew scripts.
diff --git a/Library/Homebrew/cleanup.rb b/Library/Homebrew/cleanup.rb
index eec28b3fe8..782d8447be 100644
--- a/Library/Homebrew/cleanup.rb
+++ b/Library/Homebrew/cleanup.rb
@@ -162,10 +162,21 @@ module Homebrew
         cleanup.periodic_clean!
       elsif f.latest_version_installed? && !cleanup.skip_clean_formula?(f)
         ohai "Running `brew cleanup #{f}`..."
+        puts_no_install_cleanup_disable_message_if_not_already!
         cleanup.cleanup_formula(f)
       end
     end
 
+    def self.puts_no_install_cleanup_disable_message_if_not_already!
+      return if Homebrew::EnvConfig.no_env_hints?
+      return if Homebrew::EnvConfig.no_install_cleanup?
+      return if @puts_no_install_cleanup_disable_message_if_not_already
+
+      puts "Disable this behaviour by setting HOMEBREW_NO_INSTALL_CLEANUP."
+      puts "Hide these hints with HOMEBREW_NO_ENV_HINTS (see `man brew`)."
+      @puts_no_install_cleanup_disable_message_if_not_already = true
+    end
+
     def skip_clean_formula?(f)
       return false if Homebrew::EnvConfig.no_cleanup_formulae.blank?
 
@@ -194,6 +205,7 @@ module Homebrew
         ohai "`brew cleanup` has not been run in the last #{CLEANUP_DEFAULT_DAYS} days, running now..."
       end
 
+      Cleanup.puts_no_install_cleanup_disable_message_if_not_already!
       return if dry_run?
 
       clean!(quiet: true, periodic: true)
diff --git a/Library/Homebrew/env_config.rb b/Library/Homebrew/env_config.rb
index 4eececa008..4f8a95a46c 100644
--- a/Library/Homebrew/env_config.rb
+++ b/Library/Homebrew/env_config.rb
@@ -257,6 +257,10 @@ module Homebrew
                      "\n\n    *Note:* Will only try to print emoji on OS X Lion or newer.",
         boolean:     true,
       },
+      HOMEBREW_NO_ENV_HINTS:                   {
+        description: "If set, do not print any hints about changing Homebrew's behaviour with environment variables.",
+        boolean:     true,
+      },
       HOMEBREW_NO_GITHUB_API:                  {
         description: "If set, do not use the GitHub API, e.g. for searches or fetching relevant issues " \
                      "after a failed install.",
diff --git a/Library/Homebrew/upgrade.rb b/Library/Homebrew/upgrade.rb
index 7fe95653a6..eec5ba567b 100644
--- a/Library/Homebrew/upgrade.rb
+++ b/Library/Homebrew/upgrade.rb
@@ -235,6 +235,16 @@ module Homebrew
       end
     end
 
+    def self.puts_no_installed_dependents_check_disable_message_if_not_already!
+      return if Homebrew::EnvConfig.no_env_hints?
+      return if Homebrew::EnvConfig.no_installed_dependents_check?
+      return if @puts_no_installed_dependents_check_disable_message_if_not_already
+
+      puts "Disable this behaviour by setting HOMEBREW_NO_INSTALLED_DEPENDENTS_CHECK."
+      puts "Hide these hints with HOMEBREW_NO_ENV_HINTS (see `man brew`)."
+      @puts_no_installed_dependents_check_disable_message_if_not_already = true
+    end
+
     def check_installed_dependents(
       formulae,
       flags:,
@@ -249,7 +259,13 @@ module Homebrew
       quiet: false,
       verbose: false
     )
-      return if Homebrew::EnvConfig.no_installed_dependents_check?
+      if Homebrew::EnvConfig.no_installed_dependents_check?
+        opoo <<~EOS
+          HOMEBREW_NO_INSTALLED_DEPENDENTS_CHECK is set: not checking for outdated
+          dependents or dependents with broken linkage!
+        EOS
+        return
+      end
 
       installed_formulae = dry_run ? formulae : FormulaInstaller.installed.to_a
       return if installed_formulae.empty?
@@ -286,6 +302,7 @@ module Homebrew
         plural = "dependent".pluralize(upgradeable_dependents.count)
         verb = dry_run ? "Would upgrade" : "Upgrading"
         ohai "#{verb} #{upgradeable_dependents.count} #{plural}:"
+        Upgrade.puts_no_installed_dependents_check_disable_message_if_not_already!
         formulae_upgrades = upgradeable_dependents.map do |f|
           name = f.full_specified_name
           if f.optlinked?
@@ -317,7 +334,10 @@ module Homebrew
       installed_formulae = FormulaInstaller.installed.to_a
 
       # Assess the dependents tree again now we've upgraded.
-      oh1 "Checking for dependents of upgraded formulae..." unless dry_run
+      unless dry_run
+        oh1 "Checking for dependents of upgraded formulae..."
+        Upgrade.puts_no_installed_dependents_check_disable_message_if_not_already!
+      end
 
       broken_dependents = check_broken_dependents(installed_formulae)
       if broken_dependents.blank?
@@ -356,6 +376,7 @@ module Homebrew
         count = reinstallable_broken_dependents.count
         plural = "dependent".pluralize(reinstallable_broken_dependents.count)
         ohai "Reinstalling #{count} #{plural} with broken linkage from source:"
+        Upgrade.puts_no_installed_dependents_check_disable_message_if_not_already!
         puts reinstallable_broken_dependents.map(&:full_specified_name)
                                             .join(", ")
       end
diff --git a/docs/Manpage.md b/docs/Manpage.md
index 5d3bd7640e..88f1c5d22b 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -2095,6 +2095,9 @@ example, run `export HOMEBREW_NO_INSECURE_REDIRECT=1` rather than just
 
     *Note:* Will only try to print emoji on OS X Lion or newer.
 
+- `HOMEBREW_NO_ENV_HINTS`
+  <br>If set, do not print any hints about changing Homebrew's behaviour with environment variables.
+
 - `HOMEBREW_NO_GITHUB_API`
   <br>If set, do not use the GitHub API, e.g. for searches or fetching relevant issues after a failed install.
 
diff --git a/manpages/brew.1 b/manpages/brew.1
index 0b5c70f663..3d675fde6c 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -3041,6 +3041,12 @@ If set, do not print \fBHOMEBREW_INSTALL_BADGE\fR on a successful build\.
 \fINote:\fR Will only try to print emoji on OS X Lion or newer\.
 .
 .TP
+\fBHOMEBREW_NO_ENV_HINTS\fR
+.
+.br
+If set, do not print any hints about changing Homebrew\'s behaviour with environment variables\.
+.
+.TP
 \fBHOMEBREW_NO_GITHUB_API\fR
 .
 .br