For deleting a branch, the "Delete Reference" permission is sufficient.

Bug: Issue 7490
Change-Id: Ic7f1bb9793ac42de6857da24149f2f3959259754
diff --git a/Documentation/access-control.txt b/Documentation/access-control.txt
index f64f739..9a849dc 100644
--- a/Documentation/access-control.txt
+++ b/Documentation/access-control.txt
@@ -602,7 +602,7 @@
 
 * Force option
 +
-Allows an existing branch to be deleted. Since a force push is
+Implies <<category_delete,Delete Reference>>. Since a force push is
 effectively a delete immediately followed by a create, but performed
 atomically on the server and logged, this option also permits forced
 push updates to branches.  Enabling this option allows existing commits
diff --git a/Documentation/project-configuration.txt b/Documentation/project-configuration.txt
index 54ddcff..2d3fd66 100644
--- a/Documentation/project-configuration.txt
+++ b/Documentation/project-configuration.txt
@@ -272,13 +272,20 @@
 - in the Web UI under 'Projects' > 'List' > <project> > 'Branches'
 - via the link:rest-api-projects.html#delete-branch[Delete Branch]
   REST endpoint
-- by using a git client to force push nothing to an existing branch
+- by using a git client
++
+----
+  $ git push origin --delete refs/heads/<branch-to-delete>
+----
++
+another method, by force pushing nothing to an existing branch:
 +
 ----
   $ git push --force origin :refs/heads/<branch-to-delete>
 ----
 
 To be able to delete branches, the user must have the
+link:access-control.html#category_delete[Delete Reference] or the
 link:access-control.html#category_push[Push] access right with the
 `force` option. In addition, project owners and Gerrit administrators
 can delete branches from the Web UI or via REST even without having the
diff --git a/gerrit-server/src/main/java/com/google/gerrit/server/git/ReceiveCommits.java b/gerrit-server/src/main/java/com/google/gerrit/server/git/ReceiveCommits.java
index 399dfc7..f4659d3 100644
--- a/gerrit-server/src/main/java/com/google/gerrit/server/git/ReceiveCommits.java
+++ b/gerrit-server/src/main/java/com/google/gerrit/server/git/ReceiveCommits.java
@@ -201,7 +201,8 @@
     UPDATE(
         "You are not allowed to perform this operation.\n"
             + "To push into this reference you need 'Push' rights."),
-    DELETE("You need 'Push' rights with the 'Force Push'\nflag set to delete references."),
+    DELETE("You need 'Delete Reference' rights or 'Push' rights with the \n"
+            + "'Force Push' flag set to delete references."),
     DELETE_CHANGES("Cannot delete from '" + REFS_CHANGES + "'"),
     CODE_REVIEW(
         "You need 'Push' rights to upload code review requests.\n"