diff --git a/src/timezone/localtime.c b/src/timezone/localtime.c
index e499ba62f6777c4f16a9b816c2e2707f3ff5088a..8b332a126168a51ecb3f5c47ce55de0fde697e93 100644
--- a/src/timezone/localtime.c
+++ b/src/timezone/localtime.c
@@ -978,20 +978,21 @@ timesub(const pg_time_t *timep, long offset,
 }
 
 /*
- * Find the next DST transition time at or after the given time
+ * Find the next DST transition time after the given time
  *
  * *timep is the input value, the other parameters are output values.
  *
  * When the function result is 1, *boundary is set to the time_t
- * representation of the next DST transition time at or after *timep,
+ * representation of the next DST transition time after *timep,
  * *before_gmtoff and *before_isdst are set to the GMT offset and isdst
- * state prevailing just before that boundary, and *after_gmtoff and
- * *after_isdst are set to the state prevailing just after that boundary.
+ * state prevailing just before that boundary (in particular, the state
+ * prevailing at *timep), and *after_gmtoff and *after_isdst are set to
+ * the state prevailing just after that boundary.
  *
- * When the function result is 0, there is no known DST transition at or
+ * When the function result is 0, there is no known DST transition
  * after *timep, but *before_gmtoff and *before_isdst indicate the GMT
  * offset and isdst state prevailing at *timep.  (This would occur in
- * DST-less time zones, for example.)
+ * DST-less time zones, or if a zone has permanently ceased using DST.)
  *
  * A function result of -1 indicates failure (this case does not actually
  * occur in our current implementation).
@@ -1027,16 +1028,16 @@ pg_next_dst_boundary(const pg_time_t *timep,
 		*before_isdst = ttisp->tt_isdst;
 		return 0;
 	}
-	if (t > sp->ats[sp->timecnt - 1])
+	if (t >= sp->ats[sp->timecnt - 1])
 	{
-		/* No known transition >= t, so use last known segment's type */
+		/* No known transition > t, so use last known segment's type */
 		i = sp->types[sp->timecnt - 1];
 		ttisp = &sp->ttis[i];
 		*before_gmtoff = ttisp->tt_gmtoff;
 		*before_isdst = ttisp->tt_isdst;
 		return 0;
 	}
-	if (t <= sp->ats[0])
+	if (t < sp->ats[0])
 	{
 		/* For "before", use lowest-numbered standard type */
 		i = 0;
@@ -1057,9 +1058,9 @@ pg_next_dst_boundary(const pg_time_t *timep,
 		*after_isdst = ttisp->tt_isdst;
 		return 1;
 	}
-	/* Else search to find the containing segment */
+	/* Else search to find the boundary following t */
 	for (i = 1; i < sp->timecnt; ++i)
-		if (t <= sp->ats[i])
+		if (t < sp->ats[i])
 			break;
 	j = sp->types[i - 1];
 	ttisp = &sp->ttis[j];