diff --git a/src/datetime/mod.rs b/src/datetime/mod.rs
index 2e9203a307..913a219b36 100644
--- a/src/datetime/mod.rs
+++ b/src/datetime/mod.rs
@@ -1269,7 +1269,7 @@ fn test_add_sub_months() {
 }
 
 #[test]
-fn test_auto_conversion() {
+fn test_auto_conversion_fixedoffset_into_utc() {
     let utc_dt = Utc.with_ymd_and_hms(2018, 9, 5, 23, 58, 0).unwrap();
     let cdt_dt = FixedOffset::west_opt(5 * 60 * 60)
         .unwrap()
@@ -1279,6 +1279,33 @@ fn test_auto_conversion() {
     assert_eq!(utc_dt, utc_dt2);
 }
 
+#[test]
+fn test_auto_conversion_utc_into_fixedoffset() {
+    let utc_dt = Utc.with_ymd_and_hms(2018, 9, 5, 23, 58, 0).unwrap();
+    let cdt_dt = FixedOffset::west_opt(5 * 60 * 60)
+        .unwrap()
+        .with_ymd_and_hms(2018, 9, 5, 18, 58, 0)
+        .unwrap();
+    let cdt_dt2: DateTime<FixedOffset> = utc_dt.into();
+    assert_eq!(cdt_dt, cdt_dt2);
+}
+
+#[cfg(feature = "clock")]
+#[test]
+fn test_auto_conversion_local_into_utc() {
+    let loc_dt = Local.with_ymd_and_hms(2020, 1, 2, 3, 4, 5).unwrap();
+    let utc_dt: DateTime<Utc> = loc_dt.into();
+    assert_eq!(utc_dt, loc_dt);
+}
+
+#[cfg(feature = "clock")]
+#[test]
+fn test_auto_conversion_utc_into_local() {
+    let utc_dt = Utc.with_ymd_and_hms(2020, 1, 2, 3, 4, 5).unwrap();
+    let loc_dt: DateTime<Local> = utc_dt.into();
+    assert_eq!(utc_dt, loc_dt);
+}
+
 #[cfg(all(test, any(feature = "rustc-serialize", feature = "serde")))]
 fn test_encodable_json<FUtc, FFixed, E>(to_string_utc: FUtc, to_string_fixed: FFixed)
 where