diff --git a/rakefiles/helpers.rb b/rakefiles/helpers.rb
index c023481f54..f344aa2042 100644
--- a/rakefiles/helpers.rb
+++ b/rakefiles/helpers.rb
@@ -14,16 +14,31 @@ def report_dir_path(dir)
     return File.join(REPORT_DIR, dir.to_s)
 end
 
-def when_changed(unchanged_message, *files)
-    Rake::Task[PREREQS_MD5_DIR].invoke
-    cache_file = File.join(PREREQS_MD5_DIR, files[0].gsub(/\W+/, '-').sub(/-+$/, '')) + '.md5'
+def compute_fingerprint(files, dirs)
     digest = Digest::MD5.new()
+
+    # Digest the contents of all the files.
     Dir[*files].select{|file| File.file?(file)}.each do |file|
         digest.file(file)
     end
-    if !File.exists?(cache_file) or digest.hexdigest != File.read(cache_file)
+
+    # Digest the names of the files in all the dirs.
+    dirs.each do |dir|
+        file_names = Dir.entries(dir).sort.join(" ")
+        digest.update(file_names)
+    end
+
+    digest.hexdigest
+end
+
+# Hash the contents of all the files, and the names of files in the dirs.
+# Run the block if they've changed.
+def when_changed(unchanged_message, files, dirs=[])
+    Rake::Task[PREREQS_MD5_DIR].invoke
+    cache_file = File.join(PREREQS_MD5_DIR, files[0].gsub(/\W+/, '-').sub(/-+$/, '')) + '.md5'
+    if !File.exists?(cache_file) or compute_fingerprint(files, dirs) != File.read(cache_file)
         yield
-        File.write(cache_file, digest.hexdigest)
+        File.write(cache_file, compute_fingerprint(files, dirs))
     elsif !unchanged_message.empty?
         puts unchanged_message
     end
diff --git a/rakefiles/prereqs.rake b/rakefiles/prereqs.rake
index 7cb509569f..f453372065 100644
--- a/rakefiles/prereqs.rake
+++ b/rakefiles/prereqs.rake
@@ -1,5 +1,4 @@
 require './rakefiles/helpers.rb'
-require 'tempfile'
 
 PREREQS_MD5_DIR = ENV["PREREQ_CACHE_DIR"] || File.join(REPO_ROOT, '.prereqs_cache')
 
@@ -13,7 +12,7 @@ task :install_prereqs => [:install_node_prereqs, :install_ruby_prereqs, :install
 desc "Install all node prerequisites for the lms and cms"
 task :install_node_prereqs => "ws:migrate" do
     unchanged = 'Node requirements unchanged, nothing to install'
-    when_changed(unchanged, 'package.json') do
+    when_changed(unchanged, ['package.json']) do
         sh('npm install')
     end unless ENV['NO_PREREQ_INSTALL']
 end
@@ -21,26 +20,23 @@ end
 desc "Install all ruby prerequisites for the lms and cms"
 task :install_ruby_prereqs => "ws:migrate" do
     unchanged = 'Ruby requirements unchanged, nothing to install'
-    when_changed(unchanged, 'Gemfile') do
+    when_changed(unchanged, ['Gemfile']) do
         sh('bundle install')
     end unless ENV['NO_PREREQ_INSTALL']
 end
 
 desc "Install all python prerequisites for the lms and cms"
 task :install_python_prereqs => "ws:migrate" do
-    Tempfile.open('pyinstalled') do |pyinstalled|
-        # Read the names of everything in site-packages, and include them in the fingerprint.
-        `python -c 'import os; import distutils.sysconfig as dusc; print sorted(os.listdir(dusc.get_python_lib()))' > #{pyinstalled.path}`
-        unchanged = 'Python requirements unchanged, nothing to install'
-        when_changed(unchanged, 'requirements/**/*', pyinstalled.path) do
-            ENV['PIP_DOWNLOAD_CACHE'] ||= '.pip_download_cache'
-            sh('pip install --exists-action w -r requirements/edx/base.txt')
-            sh('pip install --exists-action w -r requirements/edx/post.txt')
-            # requirements/private.txt is used to install our libs as
-            # working dirs, or for personal-use tools.
-            if File.file?("requirements/private.txt")
-                sh('pip install -r requirements/private.txt')
-            end
+    site_packages_dir = `python -c 'import os; import distutils.sysconfig as dusc; print dusc.get_python_lib()'`.chomp
+    unchanged = 'Python requirements unchanged, nothing to install'
+    when_changed(unchanged, ['requirements/**/*'], [site_packages_dir]) do
+        ENV['PIP_DOWNLOAD_CACHE'] ||= '.pip_download_cache'
+        sh('pip install --exists-action w -r requirements/edx/base.txt')
+        sh('pip install --exists-action w -r requirements/edx/post.txt')
+        # requirements/private.txt is used to install our libs as
+        # working dirs, or for personal-use tools.
+        if File.file?("requirements/private.txt")
+            sh('pip install -r requirements/private.txt')
         end
     end unless ENV['NO_PREREQ_INSTALL']
 end