diff --git a/src/datetime/mod.rs b/src/datetime/mod.rs
index 78c3974ccb..3dfe8a1e30 100644
--- a/src/datetime/mod.rs
+++ b/src/datetime/mod.rs
@@ -579,12 +579,18 @@ impl DateTime<Utc> {
     /// This is guaranteed to round-trip with regard to [`timestamp`](DateTime::timestamp) and
     /// [`timestamp_subsec_nanos`](DateTime::timestamp_subsec_nanos).
     ///
-    /// Returns `None` on out-of-range number of seconds and/or
-    /// invalid nanosecond, otherwise returns `Some(DateTime {...})`.
-    ///
     /// If you need to create a `DateTime` with a [`TimeZone`] different from [`Utc`], use
     /// [`TimeZone::timestamp_opt`] or [`DateTime::with_timezone`].
     ///
+    /// The nanosecond part can exceed 1,000,000,000 in order to represent a
+    /// [leap second](NaiveTime#leap-second-handling), but only when `secs % 60 == 59`.
+    /// (The true "UNIX timestamp" cannot represent a leap second unambiguously.)
+    ///
+    /// # Errors
+    ///
+    /// Returns `None` on out-of-range number of seconds and/or
+    /// invalid nanosecond, otherwise returns `Some(DateTime {...})`.
+    ///
     /// # Example
     ///
     /// ```
diff --git a/src/naive/datetime/mod.rs b/src/naive/datetime/mod.rs
index 387f03207d..32367e0372 100644
--- a/src/naive/datetime/mod.rs
+++ b/src/naive/datetime/mod.rs
@@ -110,9 +110,9 @@ impl NaiveDateTime {
     /// For a non-naive version of this function see
     /// [`TimeZone::timestamp`](../offset/trait.TimeZone.html#method.timestamp).
     ///
-    /// The nanosecond part can exceed 1,000,000,000 in order to represent the
-    /// [leap second](./struct.NaiveTime.html#leap-second-handling). (The true "UNIX
-    /// timestamp" cannot represent a leap second unambiguously.)
+    /// The nanosecond part can exceed 1,000,000,000 in order to represent a
+    /// [leap second](NaiveTime#leap-second-handling), but only when `secs % 60 == 59`.
+    /// (The true "UNIX timestamp" cannot represent a leap second unambiguously.)
     ///
     /// # Panics
     ///
@@ -196,8 +196,8 @@ impl NaiveDateTime {
     /// since the midnight UTC on January 1, 1970 (aka "UNIX timestamp")
     /// and the number of nanoseconds since the last whole non-leap second.
     ///
-    /// The nanosecond part can exceed 1,000,000,000
-    /// in order to represent the [leap second](./struct.NaiveTime.html#leap-second-handling).
+    /// The nanosecond part can exceed 1,000,000,000 in order to represent a
+    /// [leap second](NaiveTime#leap-second-handling), but only when `secs % 60 == 59`.
     /// (The true "UNIX timestamp" cannot represent a leap second unambiguously.)
     ///
     /// # Errors
@@ -216,8 +216,9 @@ impl NaiveDateTime {
     ///
     /// assert!(from_timestamp_opt(0, 0).is_some());
     /// assert!(from_timestamp_opt(0, 999_999_999).is_some());
-    /// assert!(from_timestamp_opt(0, 1_500_000_000).is_some()); // leap second
-    /// assert!(from_timestamp_opt(0, 2_000_000_000).is_none());
+    /// assert!(from_timestamp_opt(0, 1_500_000_000).is_none()); // invalid leap second
+    /// assert!(from_timestamp_opt(59, 1_500_000_000).is_some()); // leap second
+    /// assert!(from_timestamp_opt(59, 2_000_000_000).is_none());
     /// assert!(from_timestamp_opt(i64::MAX, 0).is_none());
     /// ```
     #[inline]
diff --git a/src/naive/time/mod.rs b/src/naive/time/mod.rs
index 4e854b2418..6bc73135b7 100644
--- a/src/naive/time/mod.rs
+++ b/src/naive/time/mod.rs
@@ -420,8 +420,8 @@ impl NaiveTime {
 
     /// Makes a new `NaiveTime` from the number of seconds since midnight and nanosecond.
     ///
-    /// The nanosecond part can exceed 1,000,000,000
-    /// in order to represent the [leap second](#leap-second-handling).
+    /// The nanosecond part is allowed exceed 1,000,000,000 in order to represent a
+    /// [leap second](#leap-second-handling), but only when `secs % 60 == 59`.
     ///
     /// # Panics
     ///
@@ -435,8 +435,8 @@ impl NaiveTime {
 
     /// Makes a new `NaiveTime` from the number of seconds since midnight and nanosecond.
     ///
-    /// The nanosecond part can exceed 1,000,000,000
-    /// in order to represent the [leap second](#leap-second-handling).
+    /// The nanosecond part is allowed exceed 1,000,000,000 in order to represent a
+    /// [leap second](#leap-second-handling), but only when `secs % 60 == 59`.
     ///
     /// # Errors
     ///
@@ -458,8 +458,10 @@ impl NaiveTime {
     #[inline]
     #[must_use]
     pub const fn from_num_seconds_from_midnight_opt(secs: u32, nano: u32) -> Option<NaiveTime> {
-        if secs >= 86_400 || nano >= 2_000_000_000 {
-            return None;
+        if secs >= 86_400 || nano >= 1_000_000_000 {
+            if !(secs < 86_400 && secs % 60 == 59 && nano < 2_000_000_000) {
+                return None;
+            }
         }
         Some(NaiveTime { secs, frac: nano })
     }
diff --git a/src/offset/mod.rs b/src/offset/mod.rs
index 419550e292..7f5857b234 100644
--- a/src/offset/mod.rs
+++ b/src/offset/mod.rs
@@ -347,6 +347,12 @@ pub trait TimeZone: Sized + Clone {
     /// since January 1, 1970 0:00:00 UTC (aka "UNIX timestamp")
     /// and the number of nanoseconds since the last whole non-leap second.
     ///
+    /// The nanosecond part can exceed 1,000,000,000 in order to represent a
+    /// [leap second](NaiveTime#leap-second-handling), but only when `secs % 60 == 59`.
+    /// (The true "UNIX timestamp" cannot represent a leap second unambiguously.)
+    ///
+    /// # Panics
+    ///
     /// Panics on the out-of-range number of seconds and/or invalid nanosecond,
     /// for a non-panicking version see [`timestamp_opt`](#method.timestamp_opt).
     #[deprecated(since = "0.4.23", note = "use `timestamp_opt()` instead")]
@@ -358,6 +364,12 @@ pub trait TimeZone: Sized + Clone {
     /// since January 1, 1970 0:00:00 UTC (aka "UNIX timestamp")
     /// and the number of nanoseconds since the last whole non-leap second.
     ///
+    /// The nanosecond part can exceed 1,000,000,000 in order to represent a
+    /// [leap second](NaiveTime#leap-second-handling), but only when `secs % 60 == 59`.
+    /// (The true "UNIX timestamp" cannot represent a leap second unambiguously.)
+    ///
+    /// # Errors
+    ///
     /// Returns `LocalResult::None` on out-of-range number of seconds and/or
     /// invalid nanosecond, otherwise always returns `LocalResult::Single`.
     ///