diff --git a/src/backend/access/heap/heapam.c b/src/backend/access/heap/heapam.c
index 4fdb549099..791958a543 100644
--- a/src/backend/access/heap/heapam.c
+++ b/src/backend/access/heap/heapam.c
@@ -6800,9 +6800,10 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 						  xl_heap_freeze_tuple *frz, bool *totally_frozen_p)
 {
 	bool		changed = false;
-	bool		freeze_xmax = false;
+	bool		xmin_frozen = false;	/* is xmin frozen after this? */
+	bool		freeze_xmax = false;	/* whether to freeze xmax now */
+	bool		xmax_frozen = false;	/* ix xmax frozen after this? */
 	TransactionId xid;
-	bool		totally_frozen = true;
 
 	frz->frzflags = 0;
 	frz->t_infomask2 = tuple->t_infomask2;
@@ -6829,10 +6830,11 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 
 			frz->t_infomask |= HEAP_XMIN_FROZEN;
 			changed = true;
+			xmin_frozen = true;
 		}
-		else
-			totally_frozen = false;
 	}
+	else if (HeapTupleHeaderXminFrozen(tuple))
+		xmin_frozen = true;
 
 	/*
 	 * Process xmax.  To thoroughly examine the current Xmax value we need to
@@ -6870,7 +6872,6 @@ 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)
 		{
@@ -6892,7 +6893,6 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 			frz->xmax = newxmax;
 
 			changed = true;
-			totally_frozen = false;
 		}
 		else
 		{
@@ -6923,9 +6923,10 @@ 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)))
+		xmax_frozen = true;
 
 	if (freeze_xmax)
 	{
@@ -6941,6 +6942,7 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 		frz->t_infomask2 &= ~HEAP_HOT_UPDATED;
 		frz->t_infomask2 &= ~HEAP_KEYS_UPDATED;
 		changed = true;
+		xmax_frozen = true;
 	}
 
 	/*
@@ -6981,7 +6983,7 @@ heap_prepare_freeze_tuple(HeapTupleHeader tuple,
 		}
 	}
 
-	*totally_frozen_p = totally_frozen;
+	*totally_frozen_p = xmin_frozen && xmax_frozen;
 	return changed;
 }