diff --git a/openssl/src/ssl/callbacks.rs b/openssl/src/ssl/callbacks.rs
index 33032ec8..26aa8b86 100644
--- a/openssl/src/ssl/callbacks.rs
+++ b/openssl/src/ssl/callbacks.rs
@@ -1,6 +1,5 @@
 use ffi;
 use libc::{c_char, c_int, c_uchar, c_uint, c_void};
-use std::any::Any;
 use std::ffi::CStr;
 use std::ptr;
 use std::slice;
@@ -18,7 +17,7 @@ use x509::X509StoreContextRef;
 
 pub extern "C" fn raw_verify<F>(preverify_ok: c_int, x509_ctx: *mut ffi::X509_STORE_CTX) -> c_int
 where
-    F: Fn(bool, &mut X509StoreContextRef) -> bool + Any + 'static + Sync + Send,
+    F: Fn(bool, &mut X509StoreContextRef) -> bool + 'static + Sync + Send,
 {
     unsafe {
         let idx = ffi::SSL_get_ex_data_X509_STORE_CTX_idx();
@@ -44,7 +43,6 @@ pub extern "C" fn raw_psk<F>(
 ) -> c_uint
 where
     F: Fn(&mut SslRef, Option<&[u8]>, &mut [u8], &mut [u8]) -> Result<usize, ErrorStack>
-        + Any
         + 'static
         + Sync
         + Send,
@@ -74,7 +72,7 @@ pub extern "C" fn ssl_raw_verify<F>(
     x509_ctx: *mut ffi::X509_STORE_CTX,
 ) -> c_int
 where
-    F: Fn(bool, &mut X509StoreContextRef) -> bool + Any + 'static + Sync + Send,
+    F: Fn(bool, &mut X509StoreContextRef) -> bool + 'static + Sync + Send,
 {
     unsafe {
         let idx = ffi::SSL_get_ex_data_X509_STORE_CTX_idx();
@@ -90,7 +88,7 @@ where
 
 pub extern "C" fn raw_sni<F>(ssl: *mut ffi::SSL, al: *mut c_int, _arg: *mut c_void) -> c_int
 where
-    F: Fn(&mut SslRef) -> Result<(), SniError> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef) -> Result<(), SniError> + 'static + Sync + Send,
 {
     unsafe {
         let ssl_ctx = ffi::SSL_get_SSL_CTX(ssl);
@@ -175,7 +173,7 @@ pub unsafe extern "C" fn raw_tmp_dh<F>(
     keylength: c_int,
 ) -> *mut ffi::DH
 where
-    F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + 'static + Sync + Send,
 {
     let ctx = ffi::SSL_get_SSL_CTX(ssl);
     let callback = ffi::SSL_CTX_get_ex_data(ctx, get_callback_idx::<F>());
@@ -202,7 +200,7 @@ pub unsafe extern "C" fn raw_tmp_ecdh<F>(
     keylength: c_int,
 ) -> *mut ffi::EC_KEY
 where
-    F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + 'static + Sync + Send,
 {
     let ctx = ffi::SSL_get_SSL_CTX(ssl);
     let callback = ffi::SSL_CTX_get_ex_data(ctx, get_callback_idx::<F>());
@@ -228,7 +226,7 @@ pub unsafe extern "C" fn raw_tmp_dh_ssl<F>(
     keylength: c_int,
 ) -> *mut ffi::DH
 where
-    F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + 'static + Sync + Send,
 {
     let callback = ffi::SSL_get_ex_data(ssl, get_ssl_callback_idx::<F>());
     let callback = &*(callback as *mut F);
@@ -254,7 +252,7 @@ pub unsafe extern "C" fn raw_tmp_ecdh_ssl<F>(
     keylength: c_int,
 ) -> *mut ffi::EC_KEY
 where
-    F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + 'static + Sync + Send,
 {
     let callback = ffi::SSL_get_ex_data(ssl, get_ssl_callback_idx::<F>());
     let callback = &*(callback as *mut F);
@@ -275,7 +273,7 @@ where
 
 pub unsafe extern "C" fn raw_tlsext_status<F>(ssl: *mut ffi::SSL, _: *mut c_void) -> c_int
 where
-    F: Fn(&mut SslRef) -> Result<bool, ErrorStack> + Any + 'static + Sync + Send,
+    F: Fn(&mut SslRef) -> Result<bool, ErrorStack> + 'static + Sync + Send,
 {
     let ssl_ctx = ffi::SSL_get_SSL_CTX(ssl as *const _);
     let callback = ffi::SSL_CTX_get_ex_data(ssl_ctx, get_callback_idx::<F>());
diff --git a/openssl/src/ssl/error.rs b/openssl/src/ssl/error.rs
index 358a88b0..64941f18 100644
--- a/openssl/src/ssl/error.rs
+++ b/openssl/src/ssl/error.rs
@@ -1,4 +1,3 @@
-use std::any::Any;
 use std::error;
 use std::error::Error as StdError;
 use std::fmt;
@@ -107,7 +106,7 @@ pub enum HandshakeError<S> {
     WouldBlock(MidHandshakeSslStream<S>),
 }
 
-impl<S: Any + fmt::Debug> StdError for HandshakeError<S> {
+impl<S: fmt::Debug> StdError for HandshakeError<S> {
     fn description(&self) -> &str {
         match *self {
             HandshakeError::SetupFailure(_) => "stream setup failed",
@@ -124,7 +123,7 @@ impl<S: Any + fmt::Debug> StdError for HandshakeError<S> {
     }
 }
 
-impl<S: Any + fmt::Debug> fmt::Display for HandshakeError<S> {
+impl<S: fmt::Debug> fmt::Display for HandshakeError<S> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         f.write_str(StdError::description(self))?;
         match *self {
diff --git a/openssl/src/ssl/mod.rs b/openssl/src/ssl/mod.rs
index c59ad8d8..7915748d 100644
--- a/openssl/src/ssl/mod.rs
+++ b/openssl/src/ssl/mod.rs
@@ -74,7 +74,6 @@ use ffi;
 use foreign_types::{ForeignType, ForeignTypeRef, Opaque};
 use libc::{c_int, c_long, c_ulong, c_void};
 use libc::{c_uchar, c_uint};
-use std::any::Any;
 use std::any::TypeId;
 use std::cmp;
 use std::collections::HashMap;
@@ -351,7 +350,7 @@ lazy_static! {
 // Creates a static index for user data of type T
 // Registers a destructor for the data which will be called
 // when context is freed
-fn get_callback_idx<T: Any + 'static>() -> c_int {
+fn get_callback_idx<T: 'static>() -> c_int {
     *INDEXES
         .lock()
         .unwrap()
@@ -359,7 +358,7 @@ fn get_callback_idx<T: Any + 'static>() -> c_int {
         .or_insert_with(|| get_new_idx::<T>())
 }
 
-fn get_ssl_callback_idx<T: Any + 'static>() -> c_int {
+fn get_ssl_callback_idx<T: 'static>() -> c_int {
     *SSL_INDEXES
         .lock()
         .unwrap()
@@ -490,7 +489,7 @@ impl SslContextBuilder {
     pub fn set_verify_callback<F>(&mut self, mode: SslVerifyMode, verify: F)
     where
         // FIXME should take a mutable reference to the store
-        F: Fn(bool, &mut X509StoreContextRef) -> bool + Any + 'static + Sync + Send,
+        F: Fn(bool, &mut X509StoreContextRef) -> bool + 'static + Sync + Send,
     {
         unsafe {
             let verify = Box::new(verify);
@@ -516,7 +515,7 @@ impl SslContextBuilder {
     /// [`SSL_CTX_set_tlsext_servername_callback`]: https://www.openssl.org/docs/manmaster/man3/SSL_CTX_set_tlsext_servername_callback.html
     pub fn set_servername_callback<F>(&mut self, callback: F)
     where
-        F: Fn(&mut SslRef) -> Result<(), SniError> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef) -> Result<(), SniError> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);
@@ -612,7 +611,7 @@ impl SslContextBuilder {
     /// [`SSL_CTX_set_tmp_dh_callback`]: https://www.openssl.org/docs/man1.0.2/ssl/SSL_CTX_set_tmp_dh.html
     pub fn set_tmp_dh_callback<F>(&mut self, callback: F)
     where
-        F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);
@@ -650,7 +649,7 @@ impl SslContextBuilder {
     #[cfg(any(all(feature = "v101", ossl101), all(feature = "v102", ossl102)))]
     pub fn set_tmp_ecdh_callback<F>(&mut self, callback: F)
     where
-        F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);
@@ -1022,7 +1021,7 @@ impl SslContextBuilder {
     /// [`SSL_CTX_set_tlsext_status_cb`]: https://www.openssl.org/docs/man1.0.2/ssl/SSL_CTX_set_tlsext_status_cb.html
     pub fn set_status_callback<F>(&mut self, callback: F) -> Result<(), ErrorStack>
     where
-        F: Fn(&mut SslRef) -> Result<bool, ErrorStack> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef) -> Result<bool, ErrorStack> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);
@@ -1051,7 +1050,6 @@ impl SslContextBuilder {
     pub fn set_psk_callback<F>(&mut self, callback: F)
     where
         F: Fn(&mut SslRef, Option<&[u8]>, &mut [u8], &mut [u8]) -> Result<usize, ErrorStack>
-            + Any
             + 'static
             + Sync
             + Send,
@@ -1500,7 +1498,7 @@ impl SslRef {
     pub fn set_verify_callback<F>(&mut self, mode: SslVerifyMode, verify: F)
     where
         // FIXME should take a mutable reference to the x509 store
-        F: Fn(bool, &mut X509StoreContextRef) -> bool + Any + 'static + Sync + Send,
+        F: Fn(bool, &mut X509StoreContextRef) -> bool + 'static + Sync + Send,
     {
         unsafe {
             let verify = Box::new(verify);
@@ -1531,7 +1529,7 @@ impl SslRef {
     /// [`SSL_set_tmp_dh_callback`]: https://www.openssl.org/docs/man1.0.2/ssl/SSL_set_tmp_dh.html
     pub fn set_tmp_dh_callback<F>(&mut self, callback: F)
     where
-        F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef, bool, u32) -> Result<Dh, ErrorStack> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);
@@ -1564,7 +1562,7 @@ impl SslRef {
     #[cfg(any(all(feature = "v101", ossl101), all(feature = "v102", ossl102)))]
     pub fn set_tmp_ecdh_callback<F>(&mut self, callback: F)
     where
-        F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + Any + 'static + Sync + Send,
+        F: Fn(&mut SslRef, bool, u32) -> Result<EcKey, ErrorStack> + 'static + Sync + Send,
     {
         unsafe {
             let callback = Box::new(callback);