diff --git a/src/backend/access/heap/heapam.c b/src/backend/access/heap/heapam.c
index 4fdb549099..0040913730 100644
--- a/src/backend/access/heap/heapam.c
+++ b/src/backend/access/heap/heapam.c
@@ -6800,9 +6800,11 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 						  xl_heap_freeze_tuple *frz, bool *totally_frozen_p)
 {
 	bool		changed = false;
-	bool		freeze_xmax = false;
+	bool		xmin_already_frozen;
+	bool		xmax_already_frozen;
+	bool		freeze_xmin;
+	bool		freeze_xmax;
 	TransactionId xid;
-	bool		totally_frozen = true;
 
 	frz->frzflags = 0;
 	frz->t_infomask2 = tuple->t_infomask2;
@@ -6811,7 +6813,11 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 
 	/* Process xmin */
 	xid = HeapTupleHeaderGetXmin(tuple);
-	if (TransactionIdIsNormal(xid))
+
+	freeze_xmin = false;
+	if (HeapTupleHeaderXminFrozen(tuple))
+		xmin_already_frozen = true;
+	else if (TransactionIdIsNormal(xid))
 	{
 		if (TransactionIdPrecedes(xid, relfrozenxid))
 			ereport(ERROR,
@@ -6827,11 +6833,15 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 						 errmsg_internal("uncommitted xmin %u from before xid cutoff %u needs to be frozen",
 										 xid, cutoff_xid)));
 
-			frz->t_infomask |= HEAP_XMIN_FROZEN;
-			changed = true;
+			freeze_xmin = true;
 		}
-		else
-			totally_frozen = false;
+	}
+
+	if (freeze_xmin)
+	{
+		Assert(!xmin_already_frozen);
+		frz->t_infomask |= HEAP_XMIN_FROZEN;
+		changed = true;
 	}
 
 	/*
@@ -6854,9 +6864,9 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 									relfrozenxid, relminmxid,
 									cutoff_xid, cutoff_multi, &flags);
 
-		if (flags & FRM_INVALIDATE_XMAX)
-			freeze_xmax = true;
-		else if (flags & FRM_RETURN_IS_XID)
+		freeze_xmax = (flags & FRM_INVALIDATE_XMAX);
+
+		if (flags & FRM_RETURN_IS_XID)
 		{
 			/*
 			 * NB -- some of these transformations are only valid because we
@@ -6870,7 +6880,6 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 			if (flags & FRM_MARK_COMMITTED)
 				frz->t_infomask |= HEAP_XMAX_COMMITTED;
 			changed = true;
-			totally_frozen = false;
 		}
 		else if (flags & FRM_RETURN_IS_MULTI)
 		{
@@ -6892,15 +6901,11 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 			frz->xmax = newxmax;
 
 			changed = true;
-			totally_frozen = false;
-		}
-		else
-		{
-			Assert(flags & FRM_NOOP);
 		}
 	}
 	else if (TransactionIdIsNormal(xid))
 	{
+		freeze_xmax = false;
 		if (TransactionIdPrecedes(xid, relfrozenxid))
 			ereport(ERROR,
 					(errcode(ERRCODE_DATA_CORRUPTED),
@@ -6923,12 +6928,23 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 										 xid)));
 			freeze_xmax = true;
 		}
-		else
-			totally_frozen = false;
+	}
+	else if (((tuple->t_infomask & HEAP_XMAX_INVALID) == HEAP_XMAX_INVALID) ||
+			 !TransactionIdIsValid(HeapTupleHeaderGetRawXmax(tuple)))
+	{
+		freeze_xmax = false;
+		xmax_already_frozen = true;
+	}
+	else
+	{
+		/* XXX ERROR? */
+		freeze_xmax = false;
 	}
 
 	if (freeze_xmax)
 	{
+		Assert(!xmax_already_frozen);
+
 		frz->xmax = InvalidTransactionId;
 
 		/*
@@ -6981,7 +6997,8 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 		}
 	}
 
-	*totally_frozen_p = totally_frozen;
+	*totally_frozen_p = (freeze_xmin || xmin_already_frozen) &&
+						(freeze_xmax || xmax_already_frozen);
 	return changed;
 }