diff --git a/Documentation/config.txt b/Documentation/config.txt
index 90e7d10bad..1f47761c89 100644
--- a/Documentation/config.txt
+++ b/Documentation/config.txt
@@ -143,7 +143,8 @@ advice.*::
 	pushUpdateRejected::
 		Set this variable to 'false' if you want to disable
 		'pushNonFFCurrent', 'pushNonFFDefault',
-		'pushNonFFMatching', and 'pushAlreadyExists'
+		'pushNonFFMatching', 'pushAlreadyExists',
+		'pushFetchFirst', and 'pushNeedsForce'
 		simultaneously.
 	pushNonFFCurrent::
 		Advice shown when linkgit:git-push[1] fails due to a
@@ -162,6 +163,15 @@ advice.*::
 	pushAlreadyExists::
 		Shown when linkgit:git-push[1] rejects an update that
 		does not qualify for fast-forwarding (e.g., a tag.)
+	pushFetchFirst::
+		Shown when linkgit:git-push[1] rejects an update that
+		tries to overwrite a remote ref that points at an
+		object we do not have.
+	pushNeedsForce::
+		Shown when linkgit:git-push[1] rejects an update that
+		tries to overwrite a remote ref that points at an
+		object that is not a committish, or make the remote
+		ref point at an object that is not a committish.
 	statusHints::
 		Show directions on how to proceed from the current
 		state in the output of linkgit:git-status[1] and in
diff --git a/advice.c b/advice.c
index d287927280..780f58da0f 100644
--- a/advice.c
+++ b/advice.c
@@ -5,6 +5,8 @@ int advice_push_non_ff_current = 1;
 int advice_push_non_ff_default = 1;
 int advice_push_non_ff_matching = 1;
 int advice_push_already_exists = 1;
+int advice_push_fetch_first = 1;
+int advice_push_needs_force = 1;
 int advice_status_hints = 1;
 int advice_commit_before_merge = 1;
 int advice_resolve_conflict = 1;
@@ -20,6 +22,8 @@ static struct {
 	{ "pushnonffdefault", &advice_push_non_ff_default },
 	{ "pushnonffmatching", &advice_push_non_ff_matching },
 	{ "pushalreadyexists", &advice_push_already_exists },
+	{ "pushfetchfirst", &advice_push_fetch_first },
+	{ "pushneedsforce", &advice_push_needs_force },
 	{ "statushints", &advice_status_hints },
 	{ "commitbeforemerge", &advice_commit_before_merge },
 	{ "resolveconflict", &advice_resolve_conflict },
diff --git a/advice.h b/advice.h
index 8bf63563a5..fad36df467 100644
--- a/advice.h
+++ b/advice.h
@@ -8,6 +8,8 @@ extern int advice_push_non_ff_current;
 extern int advice_push_non_ff_default;
 extern int advice_push_non_ff_matching;
 extern int advice_push_already_exists;
+extern int advice_push_fetch_first;
+extern int advice_push_needs_force;
 extern int advice_status_hints;
 extern int advice_commit_before_merge;
 extern int advice_resolve_conflict;
diff --git a/builtin/push.c b/builtin/push.c
index 8491e431e4..a2b3fbed6a 100644
--- a/builtin/push.c
+++ b/builtin/push.c
@@ -220,10 +220,22 @@ static const char message_advice_checkout_pull_push[] =
 	   "(e.g. 'git pull') before pushing again.\n"
 	   "See the 'Note about fast-forwards' in 'git push --help' for details.");
 
+static const char message_advice_ref_fetch_first[] =
+	N_("Updates were rejected because the remote contains work that you do\n"
+	   "not have locally. This is usually caused by another repository pushing\n"
+	   "to the same ref. You may want to first merge the remote changes (e.g.,\n"
+	   "'git pull') before pushing again.\n"
+	   "See the 'Note about fast-forwards' in 'git push --help' for details.");
+
 static const char message_advice_ref_already_exists[] =
 	N_("Updates were rejected because the destination reference already exists\n"
 	   "in the remote.");
 
+static const char message_advice_ref_needs_force[] =
+	N_("You cannot update a remote ref that points at a non-commit object,\n"
+	   "or update a remote ref to make it point at a non-commit object,\n"
+	   "without using the '--force' option.\n");
+
 static void advise_pull_before_push(void)
 {
 	if (!advice_push_non_ff_current || !advice_push_update_rejected)
@@ -252,6 +264,20 @@ static void advise_ref_already_exists(void)
 	advise(_(message_advice_ref_already_exists));
 }
 
+static void advise_ref_fetch_first(void)
+{
+	if (!advice_push_fetch_first || !advice_push_update_rejected)
+		return;
+	advise(_(message_advice_ref_fetch_first));
+}
+
+static void advise_ref_needs_force(void)
+{
+	if (!advice_push_needs_force || !advice_push_update_rejected)
+		return;
+	advise(_(message_advice_ref_needs_force));
+}
+
 static int push_with_options(struct transport *transport, int flags)
 {
 	int err;
@@ -285,6 +311,10 @@ static int push_with_options(struct transport *transport, int flags)
 			advise_checkout_pull_push();
 	} else if (reject_reasons & REJECT_ALREADY_EXISTS) {
 		advise_ref_already_exists();
+	} else if (reject_reasons & REJECT_FETCH_FIRST) {
+		advise_ref_fetch_first();
+	} else if (reject_reasons & REJECT_NEEDS_FORCE) {
+		advise_ref_needs_force();
 	}
 
 	return 1;
diff --git a/builtin/send-pack.c b/builtin/send-pack.c
index f849e0a4a0..57a46b2654 100644
--- a/builtin/send-pack.c
+++ b/builtin/send-pack.c
@@ -44,6 +44,16 @@ static void print_helper_status(struct ref *ref)
 			msg = "non-fast forward";
 			break;
 
+		case REF_STATUS_REJECT_FETCH_FIRST:
+			res = "error";
+			msg = "fetch first";
+			break;
+
+		case REF_STATUS_REJECT_NEEDS_FORCE:
+			res = "error";
+			msg = "needs force";
+			break;
+
 		case REF_STATUS_REJECT_ALREADY_EXISTS:
 			res = "error";
 			msg = "already exists";
diff --git a/cache.h b/cache.h
index 12631a17d3..377a3df157 100644
--- a/cache.h
+++ b/cache.h
@@ -1010,6 +1010,8 @@ struct ref {
 		REF_STATUS_REJECT_NONFASTFORWARD,
 		REF_STATUS_REJECT_ALREADY_EXISTS,
 		REF_STATUS_REJECT_NODELETE,
+		REF_STATUS_REJECT_FETCH_FIRST,
+		REF_STATUS_REJECT_NEEDS_FORCE,
 		REF_STATUS_UPTODATE,
 		REF_STATUS_REMOTE_REJECT,
 		REF_STATUS_EXPECTING_REPORT
diff --git a/remote.c b/remote.c
index 969aa11690..a772e747b7 100644
--- a/remote.c
+++ b/remote.c
@@ -1322,8 +1322,12 @@ void set_ref_status_for_push(struct ref *remote_refs, int send_mirror,
 
 			if (!prefixcmp(ref->name, "refs/tags/"))
 				why = REF_STATUS_REJECT_ALREADY_EXISTS;
-			else if (!has_sha1_file(ref->old_sha1)
-				 || !ref_newer(ref->new_sha1, ref->old_sha1))
+			else if (!has_sha1_file(ref->old_sha1))
+				why = REF_STATUS_REJECT_FETCH_FIRST;
+			else if (!lookup_commit_reference_gently(ref->old_sha1, 1) ||
+				 !lookup_commit_reference_gently(ref->new_sha1, 1))
+				why = REF_STATUS_REJECT_NEEDS_FORCE;
+			else if (!ref_newer(ref->new_sha1, ref->old_sha1))
 				why = REF_STATUS_REJECT_NONFASTFORWARD;
 
 			if (!force_ref_update)
@@ -1512,7 +1516,8 @@ int ref_newer(const unsigned char *new_sha1, const unsigned char *old_sha1)
 	struct commit_list *list, *used;
 	int found = 0;
 
-	/* Both new and old must be commit-ish and new is descendant of
+	/*
+	 * Both new and old must be commit-ish and new is descendant of
 	 * old.  Otherwise we require --force.
 	 */
 	o = deref_tag(parse_object(old_sha1), NULL, 0);
diff --git a/send-pack.c b/send-pack.c
index 1c375f0a28..97ab336097 100644
--- a/send-pack.c
+++ b/send-pack.c
@@ -230,6 +230,8 @@ int send_pack(struct send_pack_args *args,
 		switch (ref->status) {
 		case REF_STATUS_REJECT_NONFASTFORWARD:
 		case REF_STATUS_REJECT_ALREADY_EXISTS:
+		case REF_STATUS_REJECT_FETCH_FIRST:
+		case REF_STATUS_REJECT_NEEDS_FORCE:
 		case REF_STATUS_UPTODATE:
 			continue;
 		default:
diff --git a/transport-helper.c b/transport-helper.c
index 965b778cb3..cb3ef7d38e 100644
--- a/transport-helper.c
+++ b/transport-helper.c
@@ -666,6 +666,16 @@ static void push_update_ref_status(struct strbuf *buf,
 			free(msg);
 			msg = NULL;
 		}
+		else if (!strcmp(msg, "fetch first")) {
+			status = REF_STATUS_REJECT_FETCH_FIRST;
+			free(msg);
+			msg = NULL;
+		}
+		else if (!strcmp(msg, "needs force")) {
+			status = REF_STATUS_REJECT_NEEDS_FORCE;
+			free(msg);
+			msg = NULL;
+		}
 	}
 
 	if (*ref)
diff --git a/transport.c b/transport.c
index 585ebcd2bf..5105562d6e 100644
--- a/transport.c
+++ b/transport.c
@@ -699,6 +699,14 @@ static int print_one_push_status(struct ref *ref, const char *dest, int count, i
 		print_ref_status('!', "[rejected]", ref, ref->peer_ref,
 						 "already exists", porcelain);
 		break;
+	case REF_STATUS_REJECT_FETCH_FIRST:
+		print_ref_status('!', "[rejected]", ref, ref->peer_ref,
+						 "fetch first", porcelain);
+		break;
+	case REF_STATUS_REJECT_NEEDS_FORCE:
+		print_ref_status('!', "[rejected]", ref, ref->peer_ref,
+						 "needs force", porcelain);
+		break;
 	case REF_STATUS_REMOTE_REJECT:
 		print_ref_status('!', "[remote rejected]", ref,
 						 ref->deletion ? NULL : ref->peer_ref,
@@ -750,6 +758,10 @@ void transport_print_push_status(const char *dest, struct ref *refs,
 				*reject_reasons |= REJECT_NON_FF_OTHER;
 		} else if (ref->status == REF_STATUS_REJECT_ALREADY_EXISTS) {
 			*reject_reasons |= REJECT_ALREADY_EXISTS;
+		} else if (ref->status == REF_STATUS_REJECT_FETCH_FIRST) {
+			*reject_reasons |= REJECT_FETCH_FIRST;
+		} else if (ref->status == REF_STATUS_REJECT_NEEDS_FORCE) {
+			*reject_reasons |= REJECT_NEEDS_FORCE;
 		}
 	}
 }
diff --git a/transport.h b/transport.h
index bfd2df5823..c818763c46 100644
--- a/transport.h
+++ b/transport.h
@@ -143,6 +143,8 @@ void transport_set_verbosity(struct transport *transport, int verbosity,
 #define REJECT_NON_FF_HEAD     0x01
 #define REJECT_NON_FF_OTHER    0x02
 #define REJECT_ALREADY_EXISTS  0x04
+#define REJECT_FETCH_FIRST     0x08
+#define REJECT_NEEDS_FORCE     0x10
 
 int transport_push(struct transport *connection,
 		   int refspec_nr, const char **refspec, int flags,