diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 02c7a0c7e1f..ca24620fd0b 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -93,6 +93,7 @@ static void ReindexPartitions(Oid relid, int options, bool isTopLevel);
 static void ReindexMultipleInternal(List *relids, int options);
 static bool ReindexRelationConcurrently(Oid relationOid, int options);
 static void update_relispartition(Oid relationId, bool newval);
+static inline void set_indexsafe_procflags(void);
 
 /*
  * callback argument type for RangeVarCallbackForReindexIndex()
@@ -384,7 +385,10 @@ CompareOpclassOptions(Datum *opts1, Datum *opts2, int natts)
  * lazy VACUUMs, because they won't be fazed by missing index entries
  * either.  (Manual ANALYZEs, however, can't be excluded because they
  * might be within transactions that are going to do arbitrary operations
- * later.)
+ * later.)  Processes running CREATE INDEX CONCURRENTLY
+ * on indexes that are neither expressional nor partial are also safe to
+ * ignore, since we know that those processes won't examine any data
+ * outside the table they're indexing.
  *
  * Also, GetCurrentVirtualXIDs never reports our own vxid, so we need not
  * check for that.
@@ -405,7 +409,8 @@ WaitForOlderSnapshots(TransactionId limitXmin, bool progress)
 	VirtualTransactionId *old_snapshots;
 
 	old_snapshots = GetCurrentVirtualXIDs(limitXmin, true, false,
-										  PROC_IS_AUTOVACUUM | PROC_IN_VACUUM,
+										  PROC_IS_AUTOVACUUM | PROC_IN_VACUUM
+										  | PROC_IN_SAFE_IC,
 										  &n_old_snapshots);
 	if (progress)
 		pgstat_progress_update_param(PROGRESS_WAITFOR_TOTAL, n_old_snapshots);
@@ -425,7 +430,8 @@ WaitForOlderSnapshots(TransactionId limitXmin, bool progress)
 
 			newer_snapshots = GetCurrentVirtualXIDs(limitXmin,
 													true, false,
-													PROC_IS_AUTOVACUUM | PROC_IN_VACUUM,
+													PROC_IS_AUTOVACUUM | PROC_IN_VACUUM
+													| PROC_IN_SAFE_IC,
 													&n_newer_snapshots);
 			for (j = i; j < n_old_snapshots; j++)
 			{
@@ -518,6 +524,7 @@ DefineIndex(Oid relationId,
 	bool		amcanorder;
 	amoptions_function amoptions;
 	bool		partitioned;
+	bool		safe_index;
 	Datum		reloptions;
 	int16	   *coloptions;
 	IndexInfo  *indexInfo;
@@ -1044,6 +1051,10 @@ DefineIndex(Oid relationId,
 		}
 	}
 
+	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
+	safe_index = indexInfo->ii_Expressions == NIL &&
+		indexInfo->ii_Predicate == NIL;
+
 	/*
 	 * Report index creation if appropriate (delay this till after most of the
 	 * error checks)
@@ -1430,6 +1441,10 @@ DefineIndex(Oid relationId,
 	CommitTransactionCommand();
 	StartTransactionCommand();
 
+	/* Tell concurrent index builds to ignore us, if index qualifies */
+	if (safe_index)
+		set_indexsafe_procflags();
+
 	/*
 	 * The index is now visible, so we can report the OID.
 	 */
@@ -1489,6 +1504,10 @@ DefineIndex(Oid relationId,
 	CommitTransactionCommand();
 	StartTransactionCommand();
 
+	/* Tell concurrent index builds to ignore us, if index qualifies */
+	if (safe_index)
+		set_indexsafe_procflags();
+
 	/*
 	 * Phase 3 of concurrent index build
 	 *
@@ -1545,6 +1564,10 @@ DefineIndex(Oid relationId,
 	CommitTransactionCommand();
 	StartTransactionCommand();
 
+	/* Tell concurrent index builds to ignore us, if index qualifies */
+	if (safe_index)
+		set_indexsafe_procflags();
+
 	/* We should now definitely not be advertising any xmin. */
 	Assert(MyProc->xmin == InvalidTransactionId);
 
@@ -3896,3 +3919,37 @@ update_relispartition(Oid relationId, bool newval)
 	heap_freetuple(tup);
 	table_close(classRel, RowExclusiveLock);
 }
+
+/*
+ * Set the PROC_IN_SAFE_IC flag in MyProc->statusFlags.
+ *
+ * When doing concurrent index builds, we can set this flag
+ * to tell other processes concurrently running CREATE
+ * INDEX CONCURRENTLY or REINDEX CONCURRENTLY to ignore us when
+ * doing their waits for concurrent snapshots.  On one hand it
+ * avoids pointlessly waiting for a process that's not interesting
+ * anyway; but more importantly it avoids deadlocks in some cases.
+ *
+ * This can be done safely only for indexes that don't execute any
+ * expressions that could access other tables, so index must not be
+ * expressional nor partial.  Caller is responsible for only calling
+ * this routine when that assumption holds true.
+ *
+ * (The flag is reset automatically at transaction end, so it must be
+ * set for each transaction.)
+ */
+static inline void
+set_indexsafe_procflags(void)
+{
+	/*
+	 * This should only be called before installing xid or xmin in MyProc;
+	 * otherwise, concurrent processes could see an Xmin that moves backwards.
+	 */
+	Assert(MyProc->xid == InvalidTransactionId &&
+		   MyProc->xmin == InvalidTransactionId);
+
+	LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
+	MyProc->statusFlags |= PROC_IN_SAFE_IC;
+	ProcGlobal->statusFlags[MyProc->pgxactoff] = MyProc->statusFlags;
+	LWLockRelease(ProcArrayLock);
+}
diff --git a/src/include/storage/proc.h b/src/include/storage/proc.h
index 00bb244340a..e75f6e81782 100644
--- a/src/include/storage/proc.h
+++ b/src/include/storage/proc.h
@@ -53,13 +53,16 @@ struct XidCache
  */
 #define		PROC_IS_AUTOVACUUM	0x01	/* is it an autovac worker? */
 #define		PROC_IN_VACUUM		0x02	/* currently running lazy vacuum */
+#define		PROC_IN_SAFE_IC		0x04	/* currently running CREATE INDEX
+										 * CONCURRENTLY on non-expressional,
+										 * non-partial index */
 #define		PROC_VACUUM_FOR_WRAPAROUND	0x08	/* set by autovac only */
 #define		PROC_IN_LOGICAL_DECODING	0x10	/* currently doing logical
 												 * decoding outside xact */
 
 /* flags reset at EOXact */
 #define		PROC_VACUUM_STATE_MASK \
-	(PROC_IN_VACUUM | PROC_VACUUM_FOR_WRAPAROUND)
+	(PROC_IN_VACUUM | PROC_IN_SAFE_IC | PROC_VACUUM_FOR_WRAPAROUND)
 
 /*
  * We allow a small number of "weak" relation locks (AccessShareLock,