diff --git a/cli/src/commands/git/fetch.rs b/cli/src/commands/git/fetch.rs
index 21b21f1d3..f806bb303 100644
--- a/cli/src/commands/git/fetch.rs
+++ b/cli/src/commands/git/fetch.rs
@@ -37,7 +37,13 @@ pub struct GitFetchArgs {
     ///
     /// By default, the specified name matches exactly. Use `glob:` prefix to
     /// expand `*` as a glob. The other wildcard characters aren't supported.
-    #[arg(long, short, alias="bookmark", default_value = "glob:*", value_parser = StringPattern::parse)]
+    #[arg(
+        long, short,
+        alias = "bookmark",
+        default_value = "glob:*",
+        value_parser = StringPattern::parse,
+        add = ArgValueCandidates::new(complete::bookmarks),
+    )]
     branch: Vec<StringPattern>,
     /// The remote to fetch from (only named remotes are supported, can be
     /// repeated)
diff --git a/cli/src/commands/git/push.rs b/cli/src/commands/git/push.rs
index 9be3eab78..b2c0c32f7 100644
--- a/cli/src/commands/git/push.rs
+++ b/cli/src/commands/git/push.rs
@@ -86,7 +86,12 @@ pub struct GitPushArgs {
     /// By default, the specified name matches exactly. Use `glob:` prefix to
     /// select bookmarks by wildcard pattern. For details, see
     /// https://martinvonz.github.io/jj/latest/revsets#string-patterns.
-    #[arg(long, short, alias="branch", value_parser = StringPattern::parse)]
+    #[arg(
+        long, short,
+        alias = "branch",
+        value_parser = StringPattern::parse,
+        add = ArgValueCandidates::new(complete::local_bookmarks),
+    )]
     bookmark: Vec<StringPattern>,
     /// Push all bookmarks (including deleted bookmarks)
     #[arg(long)]
diff --git a/cli/tests/test_completion.rs b/cli/tests/test_completion.rs
index c9484106c..659876aff 100644
--- a/cli/tests/test_completion.rs
+++ b/cli/tests/test_completion.rs
@@ -126,6 +126,19 @@ fn test_bookmark_names() {
 
     let stdout = test_env.jj_cmd_success(&repo_path, &["--", "jj", "bookmark", "untrack", "a"]);
     insta::assert_snapshot!(stdout, @"aaa-tracked@origin");
+
+    let stdout = test_env.jj_cmd_success(&repo_path, &["--", "jj", "git", "push", "-b", "a"]);
+    insta::assert_snapshot!(stdout, @r"
+    aaa-local
+    aaa-tracked
+    ");
+
+    let stdout = test_env.jj_cmd_success(&repo_path, &["--", "jj", "git", "fetch", "-b", "a"]);
+    insta::assert_snapshot!(stdout, @r"
+    aaa-local
+    aaa-tracked
+    aaa-untracked
+    ");
 }
 
 #[test]