diff --git a/.travis.yml b/.travis.yml
index f918a16fae..6f37f73a34 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -26,7 +26,7 @@ before_install:
       sudo chown -R "$USER" "$HOMEBREW_REPOSITORY";
     else
       LINUX="1";
-      export PATH="$PWD/bin:$PATH";
+      export PATH="$PWD/bin:/usr/bin:/bin";
     fi
   # umask 022 fixes Linux `brew tests` failures;
   - if [ "$LINUX" ]; then
diff --git a/Library/Homebrew/cleanup.rb b/Library/Homebrew/cleanup.rb
index 6546eb2f76..ca0aaed41b 100644
--- a/Library/Homebrew/cleanup.rb
+++ b/Library/Homebrew/cleanup.rb
@@ -293,7 +293,6 @@ module Homebrew
     def rm_ds_store(dirs = nil)
       dirs ||= begin
         Keg::MUST_EXIST_DIRECTORIES + [
-          HOMEBREW_CELLAR,
           HOMEBREW_PREFIX/"Caskroom",
         ]
       end
diff --git a/Library/Homebrew/cmd/prune.rb b/Library/Homebrew/cmd/prune.rb
index 55edc5b610..e26049e1c6 100644
--- a/Library/Homebrew/cmd/prune.rb
+++ b/Library/Homebrew/cmd/prune.rb
@@ -15,7 +15,7 @@ module Homebrew
 
     dirs = []
 
-    Keg::PRUNEABLE_DIRECTORIES.each do |dir|
+    Keg::MUST_EXIST_SUBDIRECTORIES.each do |dir|
       next unless dir.directory?
 
       dir.find do |path|
@@ -32,8 +32,7 @@ module Homebrew
               path.unlink
             end
           end
-        elsif path.directory? && !Keg::PRUNEABLE_DIRECTORIES.include?(path) &&
-              !Keg::MUST_BE_WRITABLE_DIRECTORIES.include?(path)
+        elsif path.directory? && !Keg::MUST_EXIST_SUBDIRECTORIES.include?(path)
           dirs << path
         end
       end
diff --git a/Library/Homebrew/diagnostic.rb b/Library/Homebrew/diagnostic.rb
index ddd47d85f5..eca5c3cad0 100644
--- a/Library/Homebrew/diagnostic.rb
+++ b/Library/Homebrew/diagnostic.rb
@@ -276,7 +276,7 @@ module Homebrew
       def check_for_broken_symlinks
         broken_symlinks = []
 
-        Keg::PRUNEABLE_DIRECTORIES.each do |d|
+        Keg::MUST_EXIST_SUBDIRECTORIES.each do |d|
           next unless d.directory?
 
           d.find do |path|
diff --git a/Library/Homebrew/install.rb b/Library/Homebrew/install.rb
index b2c9f8dde6..c451acd15e 100644
--- a/Library/Homebrew/install.rb
+++ b/Library/Homebrew/install.rb
@@ -18,7 +18,7 @@ module Homebrew
     end
 
     def attempt_directory_creation
-      Keg::MUST_BE_WRITABLE_DIRECTORIES.each do |dir|
+      Keg::MUST_EXIST_DIRECTORIES.each do |dir|
         begin
           FileUtils.mkdir_p(dir) unless dir.exist?
         rescue
diff --git a/Library/Homebrew/keg.rb b/Library/Homebrew/keg.rb
index 8e369fe53c..c8287b372e 100644
--- a/Library/Homebrew/keg.rb
+++ b/Library/Homebrew/keg.rb
@@ -70,27 +70,27 @@ class Keg
   ].freeze
   # TODO: remove when brew-test-bot no longer uses this
   TOP_LEVEL_DIRECTORIES = KEG_LINK_DIRECTORIES
-  PRUNEABLE_DIRECTORIES = (
-    KEG_LINK_DIRECTORIES - %w[var] + %w[var/homebrew/linked]
-  ).map { |dir| HOMEBREW_PREFIX/dir }
+  MUST_EXIST_SUBDIRECTORIES = (
+    KEG_LINK_DIRECTORIES - %w[var] + %w[
+      opt
+      var/homebrew/linked
+    ]
+  ).map { |dir| HOMEBREW_PREFIX/dir }.uniq.sort.freeze
 
   # Keep relatively in sync with
   # https://github.com/Homebrew/install/blob/master/install
-  MUST_EXIST_DIRECTORIES = (
-    (KEG_LINK_DIRECTORIES + %w[
-      opt
-    ]).map { |dir| HOMEBREW_PREFIX/dir }
-  ).freeze
+  MUST_EXIST_DIRECTORIES = MUST_EXIST_SUBDIRECTORIES + [
+    HOMEBREW_CELLAR,
+  ].uniq.sort.freeze
   MUST_BE_WRITABLE_DIRECTORIES = (
-    (KEG_LINK_DIRECTORIES + %w[
-      opt
+    %w[
       etc/bash_completion.d lib/pkgconfig
       share/aclocal share/doc share/info share/locale share/man
       share/man/man1 share/man/man2 share/man/man3 share/man/man4
       share/man/man5 share/man/man6 share/man/man7 share/man/man8
       share/zsh share/zsh/site-functions
       var/log
-    ]).map { |dir| HOMEBREW_PREFIX/dir } + [
+    ].map { |dir| HOMEBREW_PREFIX/dir } + MUST_EXIST_SUBDIRECTORIES + [
       HOMEBREW_CACHE,
       HOMEBREW_CELLAR,
       HOMEBREW_LOCKS,
@@ -98,7 +98,7 @@ class Keg
       HOMEBREW_REPOSITORY,
       Language::Python.homebrew_site_packages,
     ]
-  ).freeze
+  ).uniq.sort.freeze
 
   # These paths relative to the keg's share directory should always be real
   # directories in the prefix, never symlinks.
diff --git a/Library/Homebrew/test/spec_helper.rb b/Library/Homebrew/test/spec_helper.rb
index e34bc3a78f..95be09565c 100644
--- a/Library/Homebrew/test/spec_helper.rb
+++ b/Library/Homebrew/test/spec_helper.rb
@@ -142,9 +142,10 @@ RSpec.configure do |config|
 
       FileUtils.rm_rf [
         TEST_DIRECTORIES.map(&:children),
-        *Keg::MUST_EXIST_DIRECTORIES,
+        *Keg::MUST_EXIST_SUBDIRECTORIES,
         HOMEBREW_LINKED_KEGS,
         HOMEBREW_PINNED_KEGS,
+        HOMEBREW_PREFIX/"var",
         HOMEBREW_PREFIX/"Caskroom",
         HOMEBREW_LIBRARY/"Taps/homebrew/homebrew-cask",
         HOMEBREW_LIBRARY/"Taps/homebrew/homebrew-bar",
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index eb3a05522b..26b6788e75 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -4,10 +4,10 @@ jobs:
     vmImage: xcode9-macos10.13
   steps:
     - bash: |
-        HOMEBREW_REPOSITORY="$(brew --repo)";
-        mv "$HOMEBREW_REPOSITORY/Library/Taps" "$PWD/Library";
-        sudo rm -rf "$HOMEBREW_REPOSITORY";
-        sudo ln -s "$PWD" "$HOMEBREW_REPOSITORY";
+        HOMEBREW_REPOSITORY="$(brew --repo)"
+        mv "$HOMEBREW_REPOSITORY/Library/Taps" "$PWD/Library"
+        sudo rm -rf "$HOMEBREW_REPOSITORY"
+        sudo ln -s "$PWD" "$HOMEBREW_REPOSITORY"
         brew update-reset Library/Taps/homebrew/homebrew-core
         brew test-bot --coverage
       displayName: Run brew test-bot