diff --git a/src/builtin.c b/src/builtin.c
index 7d6f775d..96e5a222 100644
--- a/src/builtin.c
+++ b/src/builtin.c
@@ -1608,16 +1608,15 @@ static void set_tm_wday(struct tm *tm) {
    * https://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week#Gauss.27s_algorithm
    * https://cs.uwaterloo.ca/~alopez-o/math-faq/node73.html
    *
-   * Tested with dates from 1900-01-01 through 2100-01-01.  This
-   * algorithm produces the wrong day-of-the-week number for dates in
-   * the range 1900-01-01..1900-02-28, and for 2100-01-01..2100-02-28.
-   * Since this is only needed on OS X and *BSD, we might just document
-   * this.
+   * Tested against gmtime() for every date from 1600-01-01 through
+   * 2400-12-31.
    */
   int century = (1900 + tm->tm_year) / 100;
   int year = (1900 + tm->tm_year) % 100;
-  if (tm->tm_mon < 2)
-    year--;
+  if (tm->tm_mon < 2 && --year < 0) {
+    year += 100;
+    century--;
+  }
   /*
    * The month value in the wday computation below is shifted so that
    * March is 1, April is 2, .., January is 11, and February is 12.
@@ -1630,7 +1629,10 @@ static void set_tm_wday(struct tm *tm) {
   if (wday < 0)
     wday += 7;
 #if 0
-  /* See commentary above */
+  /*
+   * Off: the bundled strptime() can leave a wrong weekday here, and %a
+   * or %u can name one that does not match the date.
+   */
   assert(wday == tm->tm_wday || tm->tm_wday == 8);
 #endif
   tm->tm_wday = wday;
@@ -1666,6 +1668,7 @@ static jv f_strptime(jq_state *jq, jv a, jv b) {
 
   struct tm tm;
   memset(&tm, 0, sizeof(tm));
+  tm.tm_mday = 1; // a format without a day of the month means the 1st
   tm.tm_wday = 8; // sentinel
   tm.tm_yday = 367; // sentinel
 
@@ -1698,6 +1701,8 @@ static jv f_strptime(jq_state *jq, jv a, jv b) {
   set_tm_yday(&tm);
 #elif defined(WIN32) || !defined(HAVE_STRPTIME)
   set_tm_wday(&tm);
+  if (tm.tm_yday == 367)
+    set_tm_yday(&tm);
 #else
   if (tm.tm_wday == 8 && tm.tm_mday != 0 && tm.tm_mon >= 0 && tm.tm_mon <= 11)
     set_tm_wday(&tm);
diff --git a/tests/jq.test b/tests/jq.test
index 6086f376..b0db09fd 100644
--- a/tests/jq.test
+++ b/tests/jq.test
@@ -1988,6 +1988,15 @@ try strflocaltime("%c" * 10) catch .
 "2015-03-05T23:51:47Z"
 [[2015,2,5,23,51,47,4,63],1425599507]
 
+# a format without a day of the month gives the first of the month
+[("2024-06" | strptime("%Y-%m")), ("2024" | strptime("%Y")) | ., todate]
+null
+[[2024,5,1,0,0,0,6,152],"2024-06-01T00:00:00Z",[2024,0,1,0,0,0,1,0],"2024-01-01T00:00:00Z"]
+
+"10:15" | strptime("%H:%M")
+null
+[1900,0,1,10,15,0,1,0]
+
 # Check day-of-week and day of year computations
 # (should trip an assert if this fails)
 last(range(365 * 67)|("1970-03-01T01:02:03Z"|strptime("%Y-%m-%dT%H:%M:%SZ")|mktime) + (86400 * .)|strftime("%Y-%m-%dT%H:%M:%SZ")|strptime("%Y-%m-%dT%H:%M:%SZ"))