diff --git a/README.md b/README.md
index 12c3645..d6e07b5 100644
--- a/README.md
+++ b/README.md
@@ -230,8 +230,8 @@ first argument. The most common subcommands are:
 
 Sets the global version of Ruby to be used in all shells by writing
 the version name to the `~/.rbenv/version` file. This version can be
-overridden by a per-project `.ruby-version` file, or by setting the
-`RBENV_VERSION` environment variable.
+overridden by an application-specific `.ruby-version` file, or by
+setting the `RBENV_VERSION` environment variable.
 
     $ rbenv global 1.9.3-p327
 
@@ -243,8 +243,8 @@ currently configured global version.
 
 ### rbenv local ###
 
-Sets a local per-project Ruby version by writing the version name to
-a `.ruby-version` file in the current directory. This version
+Sets a local application-specific Ruby version by writing the version
+name to a `.ruby-version` file in the current directory. This version
 overrides the global, and can be overridden itself by setting the
 `RBENV_VERSION` environment variable or with the `rbenv shell`
 command.
@@ -264,8 +264,8 @@ read a local version specified in an `.rbenv-version` file, but a
 ### rbenv shell ###
 
 Sets a shell-specific Ruby version by setting the `RBENV_VERSION`
-environment variable in your shell. This version overrides both
-project-specific versions and the global version.
+environment variable in your shell. This version overrides
+application-specific versions and the global version.
 
     $ rbenv shell jruby-1.7.1
 
diff --git a/libexec/rbenv-local b/libexec/rbenv-local
index 9da4481..3446441 100755
--- a/libexec/rbenv-local
+++ b/libexec/rbenv-local
@@ -1,18 +1,19 @@
 #!/usr/bin/env bash
 #
-# Summary: Set or show the local directory-specific Ruby version
+# Summary: Set or show the local application-specific Ruby version
 #
 # Usage: rbenv local <version>
 #        rbenv local --unset
 #
-# Sets the local directory-specific Ruby version by writing the version
-# name to a file named `.ruby-version'.
+# Sets the local application-specific Ruby version by writing the
+# version name to a file named `.ruby-version'.
 #
 # When you run a Ruby command, rbenv will look for a `.ruby-version'
 # file in the current directory and each parent directory. If no such
 # file is found in the tree, rbenv will use the global Ruby version
-# specified with `rbenv global', or the version specified in the
-# RBENV_VERSION environment variable.
+# specified with `rbenv global'. A version specified with the
+# `RBENV_VERSION' environment variable takes precedence over local
+# and global versions.
 #
 # For backwards compatibility, rbenv will also read version
 # specifications from `.rbenv-version' files, but a `.ruby-version'
diff --git a/libexec/rbenv-sh-shell b/libexec/rbenv-sh-shell
index d49eaa5..4b89c6c 100755
--- a/libexec/rbenv-sh-shell
+++ b/libexec/rbenv-sh-shell
@@ -6,8 +6,8 @@
 #        rbenv shell --unset
 #
 # Sets a shell-specific Ruby version by setting the `RBENV_VERSION'
-# environment variable in your shell. This version overrides both
-# project-specific versions and the global version.
+# environment variable in your shell. This version overrides local
+# application-specific versions and the global version.
 #
 # <version> should be a string matching a Ruby version known to rbenv.
 # The special version string `system' will use your default system Ruby.