diff --git a/src/naive/datetime/tests.rs b/src/naive/datetime/tests.rs
index 202bdb34d3..503c24061e 100644
--- a/src/naive/datetime/tests.rs
+++ b/src/naive/datetime/tests.rs
@@ -11,7 +11,19 @@ fn test_datetime_from_timestamp_millis() {
         (1662921288123, "2022-09-11 18:34:48.123000000"),
         (1662921287890, "2022-09-11 18:34:47.890000000"),
         (-2208936075000, "1900-01-01 14:38:45.000000000"),
+        (-1, "1969-12-31 23:59:59.999000000"),
         (0, "1970-01-01 00:00:00.000000000"),
+        (1, "1970-01-01 00:00:00.001000000"),
+        (998, "1970-01-01 00:00:00.998000000"),
+        (999, "1970-01-01 00:00:00.999000000"),
+        (1000, "1970-01-01 00:00:01.000000000"),
+        (1001, "1970-01-01 00:00:01.001000000"),
+        (1002, "1970-01-01 00:00:01.002000000"),
+        (999_998, "1970-01-01 00:16:39.998000000"),
+        (999_999, "1970-01-01 00:16:39.999000000"),
+        (1_000_000, "1970-01-01 00:16:40.000000000"),
+        (1_000_001, "1970-01-01 00:16:40.001000000"),
+        (1_000_002, "1970-01-01 00:16:40.002000000"),
         (119731017000, "1973-10-17 18:36:57.000000000"),
         (1234567890000, "2009-02-13 23:31:30.000000000"),
         (2034061609000, "2034-06-16 09:06:49.000000000"),
@@ -48,7 +60,19 @@ fn test_datetime_from_timestamp_micros() {
         (1662921288123456, "2022-09-11 18:34:48.123456000"),
         (1662921287890000, "2022-09-11 18:34:47.890000000"),
         (-2208936075000000, "1900-01-01 14:38:45.000000000"),
+        (-1, "1969-12-31 23:59:59.999999000"),
         (0, "1970-01-01 00:00:00.000000000"),
+        (1, "1970-01-01 00:00:00.000001000"),
+        (998, "1970-01-01 00:00:00.000998000"),
+        (999, "1970-01-01 00:00:00.000999000"),
+        (1000, "1970-01-01 00:00:00.001000000"),
+        (1001, "1970-01-01 00:00:00.001001000"),
+        (1002, "1970-01-01 00:00:00.001002000"),
+        (999_998, "1970-01-01 00:00:00.999998000"),
+        (999_999, "1970-01-01 00:00:00.999999000"),
+        (1_000_000, "1970-01-01 00:00:01.000000000"),
+        (1_000_001, "1970-01-01 00:00:01.000001000"),
+        (1_000_002, "1970-01-01 00:00:01.000002000"),
         (119731017000000, "1973-10-17 18:36:57.000000000"),
         (1234567890000000, "2009-02-13 23:31:30.000000000"),
         (2034061609000000, "2034-06-16 09:06:49.000000000"),
@@ -77,6 +101,18 @@ fn test_datetime_from_timestamp_micros() {
         );
     }
 }
+#[test]
+fn test_datetime_from_timestamp_issue934() {
+    let min_utc = crate::DateTime::<Utc>::MIN_UTC;
+    assert_eq!(
+        NaiveDateTime::from_timestamp_millis(min_utc.timestamp_millis()).unwrap(),
+        min_utc.naive_utc()
+    );
+    assert_eq!(
+        NaiveDateTime::from_timestamp_micros(min_utc.timestamp_micros()).unwrap(),
+        min_utc.naive_utc()
+    );
+}
 
 #[test]
 fn test_datetime_from_timestamp() {