diff --git a/Documentation/git-fsck.txt b/Documentation/git-fsck.txt
index 55950d9eea9..e0eae642c10 100644
--- a/Documentation/git-fsck.txt
+++ b/Documentation/git-fsck.txt
@@ -62,9 +62,17 @@ index file, all SHA-1 references in `refs` namespace, and all reflogs
 	with --no-full.
 
 --connectivity-only::
-	Check only the connectivity of tags, commits and tree objects. By
-	avoiding to unpack blobs, this speeds up the operation, at the
-	expense of missing corrupt objects or other problematic issues.
+	Check only the connectivity of reachable objects, making sure
+	that any objects referenced by a reachable tag, commit, or tree
+	is present. This speeds up the operation by avoiding reading
+	blobs entirely (though it does still check that referenced blobs
+	exist). This will detect corruption in commits and trees, but
+	not do any semantic checks (e.g., for format errors). Corruption
+	in blob objects will not be detected at all.
++
+Unreachable tags, commits, and trees will also be accessed to find the
+tips of dangling segments of history. Use `--no-dangling` if you don't
+care about this output and want to speed it up further.
 
 --strict::
 	Enable more strict checking, namely to catch a file mode
diff --git a/builtin/fsck.c b/builtin/fsck.c
index bb4227bebc6..d26fb0a0447 100644
--- a/builtin/fsck.c
+++ b/builtin/fsck.c
@@ -235,6 +235,48 @@ static int mark_used(struct object *obj, int type, void *data, struct fsck_optio
 	return 0;
 }
 
+static void mark_unreachable_referents(const struct object_id *oid)
+{
+	struct fsck_options options = FSCK_OPTIONS_DEFAULT;
+	struct object *obj = lookup_object(the_repository, oid->hash);
+
+	if (!obj || !(obj->flags & HAS_OBJ))
+		return; /* not part of our original set */
+	if (obj->flags & REACHABLE)
+		return; /* reachable objects already traversed */
+
+	/*
+	 * Avoid passing OBJ_NONE to fsck_walk, which will parse the object
+	 * (and we want to avoid parsing blobs).
+	 */
+	if (obj->type == OBJ_NONE) {
+		enum object_type type = oid_object_info(the_repository,
+							&obj->oid, NULL);
+		if (type > 0)
+			object_as_type(the_repository, obj, type, 0);
+	}
+
+	options.walk = mark_used;
+	fsck_walk(obj, NULL, &options);
+}
+
+static int mark_loose_unreachable_referents(const struct object_id *oid,
+					    const char *path,
+					    void *data)
+{
+	mark_unreachable_referents(oid);
+	return 0;
+}
+
+static int mark_packed_unreachable_referents(const struct object_id *oid,
+					     struct packed_git *pack,
+					     uint32_t pos,
+					     void *data)
+{
+	mark_unreachable_referents(oid);
+	return 0;
+}
+
 /*
  * Check a single reachable object
  */
@@ -347,6 +389,26 @@ static void check_connectivity(void)
 	/* Traverse the pending reachable objects */
 	traverse_reachable();
 
+	/*
+	 * With --connectivity-only, we won't have actually opened and marked
+	 * unreachable objects with USED. Do that now to make --dangling, etc
+	 * accurate.
+	 */
+	if (connectivity_only && (show_dangling || write_lost_and_found)) {
+		/*
+		 * Even though we already have a "struct object" for each of
+		 * these in memory, we must not iterate over the internal
+		 * object hash as we do below. Our loop would potentially
+		 * resize the hash, making our iteration invalid.
+		 *
+		 * Instead, we'll just go back to the source list of objects,
+		 * and ignore any that weren't present in our earlier
+		 * traversal.
+		 */
+		for_each_loose_object(mark_loose_unreachable_referents, NULL, 0);
+		for_each_packed_object(mark_packed_unreachable_referents, NULL, 0);
+	}
+
 	/* Look up all the requirements, warn about missing objects.. */
 	max = get_max_object_index();
 	if (verbose)
diff --git a/t/t1450-fsck.sh b/t/t1450-fsck.sh
index c61f9721413..49f08d5b9c0 100755
--- a/t/t1450-fsck.sh
+++ b/t/t1450-fsck.sh
@@ -740,7 +740,7 @@ test_expect_success 'fsck detects truncated loose object' '
 # for each of type, we have one version which is referenced by another object
 # (and so while unreachable, not dangling), and another variant which really is
 # dangling.
-test_expect_success 'fsck notices dangling objects' '
+test_expect_success 'create dangling-object repository' '
 	git init dangling &&
 	(
 		cd dangling &&
@@ -751,12 +751,17 @@ test_expect_success 'fsck notices dangling objects' '
 		commit=$(git commit-tree $tree) &&
 		dcommit=$(git commit-tree -p $commit $tree) &&
 
-		cat >expect <<-EOF &&
+		cat >expect <<-EOF
 		dangling blob $dblob
 		dangling commit $dcommit
 		dangling tree $dtree
 		EOF
+	)
+'
 
+test_expect_success 'fsck notices dangling objects' '
+	(
+		cd dangling &&
 		git fsck >actual &&
 		# the output order is non-deterministic, as it comes from a hash
 		sort <actual >actual.sorted &&
@@ -764,6 +769,16 @@ test_expect_success 'fsck notices dangling objects' '
 	)
 '
 
+test_expect_success 'fsck --connectivity-only notices dangling objects' '
+	(
+		cd dangling &&
+		git fsck --connectivity-only >actual &&
+		# the output order is non-deterministic, as it comes from a hash
+		sort <actual >actual.sorted &&
+		test_i18ncmp expect actual.sorted
+	)
+'
+
 test_expect_success 'fsck $name notices bogus $name' '
 	test_must_fail git fsck bogus &&
 	test_must_fail git fsck $ZERO_OID