diff --git a/contrib/amcheck/verify_heapam.c b/contrib/amcheck/verify_heapam.c
index 8a8e36dde7e..827312306f6 100644
--- a/contrib/amcheck/verify_heapam.c
+++ b/contrib/amcheck/verify_heapam.c
@@ -1877,7 +1877,9 @@ check_tuple(HeapCheckContext *ctx, bool *xmin_commit_status_ok,
 /*
  * Convert a TransactionId into a FullTransactionId using our cached values of
  * the valid transaction ID range.  It is the caller's responsibility to have
- * already updated the cached values, if necessary.
+ * already updated the cached values, if necessary.  This is akin to
+ * FullTransactionIdFromAllowableAt(), but it tolerates corruption in the form
+ * of an xid before epoch 0.
  */
 static FullTransactionId
 FullTransactionIdFromXidAndCtx(TransactionId xid, const HeapCheckContext *ctx)
diff --git a/src/backend/access/transam/twophase.c b/src/backend/access/transam/twophase.c
index ab2f4a8a92f..73a80559194 100644
--- a/src/backend/access/transam/twophase.c
+++ b/src/backend/access/transam/twophase.c
@@ -929,32 +929,16 @@ TwoPhaseGetDummyProc(TransactionId xid, bool lock_held)
 /*
  * Compute the FullTransactionId for the given TransactionId.
  *
- * The wrap logic is safe here because the span of active xids cannot exceed one
- * epoch at any given time.
+ * This is safe if the xid has not yet reached COMMIT PREPARED or ROLLBACK
+ * PREPARED.  After those commands, concurrent vac_truncate_clog() may make
+ * the xid cease to qualify as allowable.  XXX Not all callers limit their
+ * calls accordingly.
  */
 static inline FullTransactionId
 AdjustToFullTransactionId(TransactionId xid)
 {
-	FullTransactionId nextFullXid;
-	TransactionId nextXid;
-	uint32		epoch;
-
 	Assert(TransactionIdIsValid(xid));
-
-	LWLockAcquire(XidGenLock, LW_SHARED);
-	nextFullXid = TransamVariables->nextXid;
-	LWLockRelease(XidGenLock);
-
-	nextXid = XidFromFullTransactionId(nextFullXid);
-	epoch = EpochFromFullTransactionId(nextFullXid);
-	if (unlikely(xid > nextXid))
-	{
-		/* Wraparound occurred, must be from a prev epoch. */
-		Assert(epoch > 0);
-		epoch--;
-	}
-
-	return FullTransactionIdFromEpochAndXid(epoch, xid);
+	return FullTransactionIdFromAllowableAt(ReadNextFullTransactionId(), xid);
 }
 
 static inline int
diff --git a/src/backend/access/transam/xlogreader.c b/src/backend/access/transam/xlogreader.c
index 3596af06172..91b6a91767d 100644
--- a/src/backend/access/transam/xlogreader.c
+++ b/src/backend/access/transam/xlogreader.c
@@ -2166,28 +2166,14 @@ RestoreBlockImage(XLogReaderState *record, uint8 block_id, char *page)
 FullTransactionId
 XLogRecGetFullXid(XLogReaderState *record)
 {
-	TransactionId xid,
-				next_xid;
-	uint32		epoch;
-
 	/*
 	 * This function is only safe during replay, because it depends on the
 	 * replay state.  See AdvanceNextFullTransactionIdPastXid() for more.
 	 */
 	Assert(AmStartupProcess() || !IsUnderPostmaster);
 
-	xid = XLogRecGetXid(record);
-	next_xid = XidFromFullTransactionId(TransamVariables->nextXid);
-	epoch = EpochFromFullTransactionId(TransamVariables->nextXid);
-
-	/*
-	 * If xid is numerically greater than next_xid, it has to be from the last
-	 * epoch.
-	 */
-	if (unlikely(xid > next_xid))
-		--epoch;
-
-	return FullTransactionIdFromEpochAndXid(epoch, xid);
+	return FullTransactionIdFromAllowableAt(TransamVariables->nextXid,
+											XLogRecGetXid(record));
 }
 
 #endif
diff --git a/src/backend/utils/adt/xid8funcs.c b/src/backend/utils/adt/xid8funcs.c
index 4736755b298..20b28b2528c 100644
--- a/src/backend/utils/adt/xid8funcs.c
+++ b/src/backend/utils/adt/xid8funcs.c
@@ -97,15 +97,11 @@ static bool
 TransactionIdInRecentPast(FullTransactionId fxid, TransactionId *extracted_xid)
 {
 	TransactionId xid = XidFromFullTransactionId(fxid);
-	uint32		now_epoch;
-	TransactionId now_epoch_next_xid;
 	FullTransactionId now_fullxid;
-	TransactionId oldest_xid;
-	FullTransactionId oldest_fxid;
+	TransactionId oldest_clog_xid;
+	FullTransactionId oldest_clog_fxid;
 
 	now_fullxid = ReadNextFullTransactionId();
-	now_epoch_next_xid = XidFromFullTransactionId(now_fullxid);
-	now_epoch = EpochFromFullTransactionId(now_fullxid);
 
 	if (extracted_xid != NULL)
 		*extracted_xid = xid;
@@ -135,52 +131,19 @@ TransactionIdInRecentPast(FullTransactionId fxid, TransactionId *extracted_xid)
 
 	/*
 	 * If fxid is not older than TransamVariables->oldestClogXid, the relevant
-	 * CLOG entry is guaranteed to still exist.  Convert
-	 * TransamVariables->oldestClogXid into a FullTransactionId to compare it
-	 * with fxid.  Determine the right epoch knowing that oldest_fxid
-	 * shouldn't be more than 2^31 older than now_fullxid.
+	 * CLOG entry is guaranteed to still exist.
+	 *
+	 * TransamVariables->oldestXid governs allowable XIDs.  Usually,
+	 * oldestClogXid==oldestXid.  It's also possible for oldestClogXid to
+	 * follow oldestXid, in which case oldestXid might advance after our
+	 * ReadNextFullTransactionId() call.  If oldestXid has advanced, that
+	 * advancement reinstated the usual oldestClogXid==oldestXid.  Whether or
+	 * not that happened, oldestClogXid is allowable relative to now_fullxid.
 	 */
-	oldest_xid = TransamVariables->oldestClogXid;
-	Assert(TransactionIdPrecedesOrEquals(oldest_xid, now_epoch_next_xid));
-	if (oldest_xid <= now_epoch_next_xid)
-	{
-		oldest_fxid = FullTransactionIdFromEpochAndXid(now_epoch, oldest_xid);
-	}
-	else
-	{
-		Assert(now_epoch > 0);
-		oldest_fxid = FullTransactionIdFromEpochAndXid(now_epoch - 1, oldest_xid);
-	}
-	return !FullTransactionIdPrecedes(fxid, oldest_fxid);
-}
-
-/*
- * Convert a TransactionId obtained from a snapshot held by the caller to a
- * FullTransactionId.  Use next_fxid as a reference FullTransactionId, so that
- * we can compute the high order bits.  It must have been obtained by the
- * caller with ReadNextFullTransactionId() after the snapshot was created.
- */
-static FullTransactionId
-widen_snapshot_xid(TransactionId xid, FullTransactionId next_fxid)
-{
-	TransactionId next_xid = XidFromFullTransactionId(next_fxid);
-	uint32		epoch = EpochFromFullTransactionId(next_fxid);
-
-	/* Special transaction ID. */
-	if (!TransactionIdIsNormal(xid))
-		return FullTransactionIdFromEpochAndXid(0, xid);
-
-	/*
-	 * The 64 bit result must be <= next_fxid, since next_fxid hadn't been
-	 * issued yet when the snapshot was created.  Every TransactionId in the
-	 * snapshot must therefore be from the same epoch as next_fxid, or the
-	 * epoch before.  We know this because next_fxid is never allow to get
-	 * more than one epoch ahead of the TransactionIds in any snapshot.
-	 */
-	if (xid > next_xid)
-		epoch--;
-
-	return FullTransactionIdFromEpochAndXid(epoch, xid);
+	oldest_clog_xid = TransamVariables->oldestClogXid;
+	oldest_clog_fxid =
+		FullTransactionIdFromAllowableAt(now_fullxid, oldest_clog_xid);
+	return !FullTransactionIdPrecedes(fxid, oldest_clog_fxid);
 }
 
 /*
@@ -420,12 +383,18 @@ pg_current_snapshot(PG_FUNCTION_ARGS)
 	nxip = cur->xcnt;
 	snap = palloc(PG_SNAPSHOT_SIZE(nxip));
 
-	/* fill */
-	snap->xmin = widen_snapshot_xid(cur->xmin, next_fxid);
-	snap->xmax = widen_snapshot_xid(cur->xmax, next_fxid);
+	/*
+	 * Fill.  This is the current backend's active snapshot, so MyProc->xmin
+	 * is <= all these XIDs.  As long as that remains so, oldestXid can't
+	 * advance past any of these XIDs.  Hence, these XIDs remain allowable
+	 * relative to next_fxid.
+	 */
+	snap->xmin = FullTransactionIdFromAllowableAt(next_fxid, cur->xmin);
+	snap->xmax = FullTransactionIdFromAllowableAt(next_fxid, cur->xmax);
 	snap->nxip = nxip;
 	for (i = 0; i < nxip; i++)
-		snap->xip[i] = widen_snapshot_xid(cur->xip[i], next_fxid);
+		snap->xip[i] =
+			FullTransactionIdFromAllowableAt(next_fxid, cur->xip[i]);
 
 	/*
 	 * We want them guaranteed to be in ascending order.  This also removes
diff --git a/src/include/access/transam.h b/src/include/access/transam.h
index 0cab8653f1b..7d82cd2eb56 100644
--- a/src/include/access/transam.h
+++ b/src/include/access/transam.h
@@ -370,6 +370,49 @@ FullTransactionIdNewer(FullTransactionId a, FullTransactionId b)
 	return b;
 }
 
+/*
+ * Compute FullTransactionId for the given TransactionId, assuming xid was
+ * between [oldestXid, nextXid] at the time when TransamVariables->nextXid was
+ * nextFullXid.  When adding calls, evaluate what prevents xid from preceding
+ * oldestXid if SetTransactionIdLimit() runs between the collection of xid and
+ * the collection of nextFullXid.
+ */
+static inline FullTransactionId
+FullTransactionIdFromAllowableAt(FullTransactionId nextFullXid,
+								 TransactionId xid)
+{
+	uint32		epoch;
+
+	/* Special transaction ID. */
+	if (!TransactionIdIsNormal(xid))
+		return FullTransactionIdFromEpochAndXid(0, xid);
+
+	Assert(TransactionIdPrecedesOrEquals(xid,
+										 XidFromFullTransactionId(nextFullXid)));
+
+	/*
+	 * The 64 bit result must be <= nextFullXid, since nextFullXid hadn't been
+	 * issued yet when xid was in the past.  The xid must therefore be from
+	 * the epoch of nextFullXid or the epoch before.  We know this because we
+	 * must remove (by freezing) an XID before assigning the XID half an epoch
+	 * ahead of it.
+	 *
+	 * The unlikely() branch hint is dubious.  It's perfect for the first 2^32
+	 * XIDs of a cluster's life.  Right at 2^32 XIDs, misprediction shoots to
+	 * 100%, then improves until perfection returns 2^31 XIDs later.  Since
+	 * current callers pass relatively-recent XIDs, expect >90% prediction
+	 * accuracy overall.  This favors average latency over tail latency.
+	 */
+	epoch = EpochFromFullTransactionId(nextFullXid);
+	if (unlikely(xid > XidFromFullTransactionId(nextFullXid)))
+	{
+		Assert(epoch != 0);
+		epoch--;
+	}
+
+	return FullTransactionIdFromEpochAndXid(epoch, xid);
+}
+
 #endif							/* FRONTEND */
 
 #endif							/* TRANSAM_H */