diff --git a/Cargo.toml b/Cargo.toml
index 9501d09..e5ac8d4 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -99,9 +99,9 @@ tokio-rustls = { version = "0.13", optional = true }
 webpki-roots = { version = "0.19", optional = true }
 
 ## cookies
-cookie_crate = { version = "0.12", package = "cookie", optional = true }
-cookie_store = { version = "0.11", optional = true }
-time = { version = "0.1.42", optional = true }
+cookie_crate = { version = "0.14", package = "cookie", optional = true }
+cookie_store = { version = "0.12", optional = true }
+time = { version = "0.2.11", optional = true }
 
 ## compression
 async-compression = { version = "0.3.0", default-features = false, features = ["stream"], optional = true }
diff --git a/src/cookie.rs b/src/cookie.rs
index bcb1eff..afb30f3 100644
--- a/src/cookie.rs
+++ b/src/cookie.rs
@@ -1,5 +1,7 @@
 //! HTTP Cookies
 
+use std::convert::TryInto;
+
 use crate::header;
 use std::fmt;
 use std::time::SystemTime;
@@ -64,12 +66,12 @@ impl<'a> Cookie<'a> {
     pub fn max_age(&self) -> Option<std::time::Duration> {
         self.0
             .max_age()
-            .map(|d| std::time::Duration::new(d.num_seconds() as u64, 0))
+            .map(|d| d.try_into().expect("time::Duration into std::time::Duration"))
     }
 
     /// The cookie expiration time.
     pub fn expires(&self) -> Option<SystemTime> {
-        self.0.expires().map(tm_to_systemtime)
+        self.0.expires().map(SystemTime::from)
     }
 }
 
@@ -98,17 +100,6 @@ impl<'a> fmt::Debug for CookieStore {
     }
 }
 
-/// Convert a time::Tm time to SystemTime.
-fn tm_to_systemtime(tm: time::Tm) -> SystemTime {
-    let seconds = tm.to_timespec().sec;
-    let duration = std::time::Duration::from_secs(seconds.abs() as u64);
-    if seconds > 0 {
-        SystemTime::UNIX_EPOCH + duration
-    } else {
-        SystemTime::UNIX_EPOCH - duration
-    }
-}
-
 /// Error representing a parse failure of a 'Set-Cookie' header.
 pub(crate) struct CookieParseError(cookie_crate::ParseError);