diff --git a/src/offset/mod.rs b/src/offset/mod.rs
index 419550e292..b7fb803cd1 100644
--- a/src/offset/mod.rs
+++ b/src/offset/mod.rs
@@ -403,12 +403,10 @@ pub trait TimeZone: Sized + Clone {
     /// };
     /// ```
     fn timestamp_millis_opt(&self, millis: i64) -> LocalResult<DateTime<Self>> {
-        let (mut secs, mut millis) = (millis / 1000, millis % 1000);
-        if millis < 0 {
-            secs -= 1;
-            millis += 1000;
+        match NaiveDateTime::from_timestamp_millis(millis) {
+            Some(dt) => LocalResult::Single(self.from_utc_datetime(&dt)),
+            None => LocalResult::None,
         }
-        self.timestamp_opt(secs, millis as u32 * 1_000_000)
     }
 
     /// Makes a new `DateTime` from the number of non-leap nanoseconds
@@ -433,6 +431,22 @@ pub trait TimeZone: Sized + Clone {
         self.timestamp_opt(secs, nanos as u32).unwrap()
     }
 
+    /// Makes a new `DateTime` from the number of non-leap microseconds
+    /// since January 1, 1970 0:00:00 UTC (aka "UNIX timestamp").
+    ///
+    /// #Example
+    /// ```
+    /// use chrono::{Utc, TimeZone};
+    ///
+    /// assert_eq!(Utc.timestamp_micros(1431648000000).unwrap().timestamp(), 1431648);
+    /// ```
+    fn timestamp_micros(&self, micros: i64) -> LocalResult<DateTime<Self>> {
+        match NaiveDateTime::from_timestamp_micros(micros) {
+            Some(dt) => LocalResult::Single(self.from_utc_datetime(&dt)),
+            None => LocalResult::None,
+        }
+    }
+
     /// Parses a string with the specified format string and returns a
     /// `DateTime` with the current offset.
     ///
@@ -558,4 +572,18 @@ mod tests {
         Utc.timestamp_nanos(i64::default());
         Utc.timestamp_nanos(i64::min_value());
     }
+
+    #[test]
+    fn test_negative_micros() {
+        let dt = Utc.timestamp_micros(-1_000_000).unwrap();
+        assert_eq!(dt.to_string(), "1969-12-31 23:59:59 UTC");
+        let dt = Utc.timestamp_micros(-999_999).unwrap();
+        assert_eq!(dt.to_string(), "1969-12-31 23:59:59.000001 UTC");
+        let dt = Utc.timestamp_micros(-1).unwrap();
+        assert_eq!(dt.to_string(), "1969-12-31 23:59:59.999999 UTC");
+        let dt = Utc.timestamp_micros(-60_000_000).unwrap();
+        assert_eq!(dt.to_string(), "1969-12-31 23:59:00 UTC");
+        let dt = Utc.timestamp_micros(-3_600_000_000).unwrap();
+        assert_eq!(dt.to_string(), "1969-12-31 23:00:00 UTC");
+    }
 }