diff --git a/libexec/pyenv-local b/libexec/pyenv-local
index 66f63c1a..7cb1a4d2 100755
--- a/libexec/pyenv-local
+++ b/libexec/pyenv-local
@@ -34,15 +34,21 @@ if [ "$1" = "--complete" ]; then
 fi
 
 versions=($@)
-PYENV_VERSION_FILE=".pyenv-version"
 
 if [ "$versions" = "--unset" ]; then
-  rm -f "$PYENV_VERSION_FILE"
+  rm -f .python-version .pyenv-version
 elif [ -n "$versions" ]; then
-  pyenv-version-file-write "$PYENV_VERSION_FILE" "${versions[@]}"
+  if [ "$(PYENV_VERSION= pyenv-version-origin)" -ef .pyenv-version ]; then
+    rm -f .pyenv-version
+    { echo "pyenv: removed existing \`.pyenv-version' file and migrated"
+      echo "       local version specification to \`.python-version' file"
+    } >&2
+  fi
+  pyenv-version-file-write .python-version "${versions[@]}"
 else
   IFS=: versions=($(
-    pyenv-version-file-read "$PYENV_VERSION_FILE" ||
+    pyenv-version-file-read .python-version ||
+    pyenv-version-file-read .pyenv-version ||
     { echo "pyenv: no local version configured for this directory"
       exit 1
     } >&2
diff --git a/libexec/pyenv-version-file b/libexec/pyenv-version-file
index cd15373b..d4c563f9 100755
--- a/libexec/pyenv-version-file
+++ b/libexec/pyenv-version-file
@@ -3,14 +3,22 @@
 set -e
 [ -n "$PYENV_DEBUG" ] && set -x
 
-root="$PYENV_DIR"
-while [ -n "$root" ]; do
-  if [ -e "${root}/.pyenv-version" ]; then
-    echo "${root}/.pyenv-version"
-    exit
-  fi
-  root="${root%/*}"
-done
+find_local_version_file() {
+  local root="$1"
+  while [ -n "$root" ]; do
+    if [ -e "${root}/.python-version" ]; then
+      echo "${root}/.python-version"
+      exit
+    elif [ -e "${root}/.pyenv-version" ]; then
+      echo "${root}/.pyenv-version"
+      exit
+    fi
+    root="${root%/*}"
+  done
+}
+
+find_local_version_file "$PYENV_DIR"
+[ "$PYENV_DIR" = "$PWD" ] || find_local_version_file "$PWD"
 
 global_version_file="${PYENV_ROOT}/version"