diff --git a/org.eclipse.jgit.test/tst/org/eclipse/jgit/api/CloneCommandTest.java b/org.eclipse.jgit.test/tst/org/eclipse/jgit/api/CloneCommandTest.java
index 6b5fe502b..1523b49ec 100644
--- a/org.eclipse.jgit.test/tst/org/eclipse/jgit/api/CloneCommandTest.java
+++ b/org.eclipse.jgit.test/tst/org/eclipse/jgit/api/CloneCommandTest.java
@@ -424,6 +424,32 @@ public void testBareCloneRepositoryOnlyOneBranch() throws Exception {
 				specs.get(0));
 	}
 
+	@Test
+	public void testCloneRepositoryOnlyOneTag() throws Exception {
+		File directory = createTempDirectory("testCloneRepositoryWithBranch");
+		CloneCommand command = Git.cloneRepository();
+		command.setBranch("tag-initial");
+		command.setBranchesToClone(
+				Collections.singletonList("refs/tags/tag-initial"));
+		command.setDirectory(directory);
+		command.setURI(fileUri());
+		Git git2 = command.call();
+		addRepoToClose(git2.getRepository());
+		assertNotNull(git2);
+		assertNull(git2.getRepository().resolve("tag-for-blob"));
+		assertNull(git2.getRepository().resolve("refs/heads/master"));
+		assertNotNull(git2.getRepository().resolve("tag-initial"));
+		ObjectId taggedCommit = db.resolve("tag-initial^{commit}");
+		assertEquals(taggedCommit.name(), git2.getRepository().getFullBranch());
+		RemoteConfig cfg = new RemoteConfig(git2.getRepository().getConfig(),
+				Constants.DEFAULT_REMOTE_NAME);
+		List<RefSpec> specs = cfg.getFetchRefSpecs();
+		assertEquals(1, specs.size());
+		assertEquals(
+				new RefSpec("+refs/tags/tag-initial:refs/tags/tag-initial"),
+				specs.get(0));
+	}
+
 	public static String allRefNames(List<Ref> refs) {
 		StringBuilder sb = new StringBuilder();
 		for (Ref f : refs) {
diff --git a/org.eclipse.jgit/src/org/eclipse/jgit/api/CloneCommand.java b/org.eclipse.jgit/src/org/eclipse/jgit/api/CloneCommand.java
index 73af8ba16..0248ba279 100644
--- a/org.eclipse.jgit/src/org/eclipse/jgit/api/CloneCommand.java
+++ b/org.eclipse.jgit/src/org/eclipse/jgit/api/CloneCommand.java
@@ -303,18 +303,25 @@ private FetchResult fetch(Repository clonedRepo, URIish u)
 	}
 
 	private List<RefSpec> calculateRefSpecs(boolean fetchAll, String dst) {
-		RefSpec wcrs = new RefSpec();
-		wcrs = wcrs.setForceUpdate(true);
-		wcrs = wcrs.setSourceDestination(Constants.R_HEADS + '*', dst);
+		RefSpec heads = new RefSpec();
+		heads = heads.setForceUpdate(true);
+		heads = heads.setSourceDestination(Constants.R_HEADS + '*', dst);
 		List<RefSpec> specs = new ArrayList<>();
 		if (!fetchAll) {
+			RefSpec tags = new RefSpec();
+			tags = tags.setForceUpdate(true);
+			tags = tags.setSourceDestination(Constants.R_TAGS + '*',
+					Constants.R_TAGS + '*');
 			for (String selectedRef : branchesToClone) {
-				if (wcrs.matchSource(selectedRef)) {
-					specs.add(wcrs.expandFromSource(selectedRef));
+				if (heads.matchSource(selectedRef)) {
+					specs.add(heads.expandFromSource(selectedRef));
+				} else if (tags.matchSource(selectedRef)) {
+					specs.add(tags.expandFromSource(selectedRef));
 				}
 			}
 		} else {
-			specs.add(wcrs);
+			// We'll fetch the tags anyway.
+			specs.add(heads);
 		}
 		return specs;
 	}
@@ -590,11 +597,15 @@ public CloneCommand setProgressMonitor(ProgressMonitor monitor) {
 	}
 
 	/**
-	 * Set whether all branches have to be fetched
+	 * Set whether all branches have to be fetched.
+	 * <p>
+	 * If {@code false}, use {@link #setBranchesToClone(Collection)} to define
+	 * what will be cloned. If neither are set, all branches will be cloned.
+	 * </p>
 	 *
 	 * @param cloneAllBranches
-	 *            true when all branches have to be fetched (indicates wildcard
-	 *            in created fetch refspec), false otherwise.
+	 *            {@code true} when all branches have to be fetched (indicates
+	 *            wildcard in created fetch refspec), {@code false} otherwise.
 	 * @return {@code this}
 	 */
 	public CloneCommand setCloneAllBranches(boolean cloneAllBranches) {
@@ -616,12 +627,17 @@ public CloneCommand setCloneSubmodules(boolean cloneSubmodules) {
 	}
 
 	/**
-	 * Set branches to clone
+	 * Set the branches or tags to clone.
+	 * <p>
+	 * This is ignored if {@link #setCloneAllBranches(boolean)
+	 * setCloneAllBranches(true)} is used. If {@code branchesToClone} is
+	 * {@code null} or empty, it's also ignored and all branches will be cloned.
+	 * </p>
 	 *
 	 * @param branchesToClone
-	 *            collection of branches to clone. Ignored when allSelected is
-	 *            true. Must be specified as full ref names (e.g.
-	 *            <code>refs/heads/master</code>).
+	 *            collection of branches to clone. Must be specified as full ref
+	 *            names (e.g. {@code refs/heads/master} or
+	 *            {@code refs/tags/v1.0.0}).
 	 * @return {@code this}
 	 */
 	public CloneCommand setBranchesToClone(Collection<String> branchesToClone) {