diff --git a/bedstead.c b/bedstead.c
index 218523a..fe87a1a 100644
--- a/bedstead.c
+++ b/bedstead.c
@@ -3155,19 +3155,18 @@ time_for_ttx(void)
 		if (!isdigit((unsigned char)epochstr[0]) ||
 		    endptr == epochstr || *endptr != '\0' ||
 		    errno == ERANGE ||
-		    /* Limit ourselves to 2000 to 10000. */
-		    epochumax < 946684800 || epochumax >= 253402300800) {
+		    /* Allow years up to 9999. */
+		    epochumax >= 253402300800) {
 			fprintf(stderr, "Invalid SOURCE_DATE_EPOCH\n");
 			return NULL;
 		}
-		epochumax -= 946684800; /* Rebase to 2000. */
 		tm.tm_isdst = -1;
 		tm.tm_sec = epochumax % 60;
 		tm.tm_min = epochumax / 60 % 60;
 		tm.tm_hour = epochumax / 3600 % 24;
 		long day = epochumax / 86400;
-		tm.tm_wday = (day - 1) % 7;
-		int y = 2000 + (day / 146097) * 400;
+		tm.tm_wday = (day + 4) % 7; /* 1970-01-01 was a Thursday. */
+		int y = 1970 + (day / 146097) * 400;
 		day = day % 146097;
 		bool ly;
 		for (;;) {