diff --git a/openssl-sys/src/lib.rs b/openssl-sys/src/lib.rs
index 2433e624..f061df26 100644
--- a/openssl-sys/src/lib.rs
+++ b/openssl-sys/src/lib.rs
@@ -1564,6 +1564,10 @@ pub unsafe fn SSL_CTX_set_tlsext_servername_callback(
     SSL_CTX_callback_ctrl(ctx, SSL_CTRL_SET_TLSEXT_SERVERNAME_CB, cb)
 }
 
+pub unsafe fn SSL_CTX_set_tlsext_servername_arg(ctx: *mut SSL_CTX, arg: *mut c_void) -> c_long {
+    SSL_CTX_ctrl(ctx, SSL_CTRL_SET_TLSEXT_SERVERNAME_ARG, 0, arg)
+}
+
 pub unsafe fn SSL_set_tlsext_host_name(s: *mut SSL, name: *mut c_char) -> c_long {
     SSL_ctrl(
         s,
diff --git a/openssl/src/ssl/callbacks.rs b/openssl/src/ssl/callbacks.rs
index f9a5aa09..c9779416 100644
--- a/openssl/src/ssl/callbacks.rs
+++ b/openssl/src/ssl/callbacks.rs
@@ -109,7 +109,8 @@ where
         let ssl = SslRef::from_ptr_mut(ssl);
         let callback_idx = SslContext::cached_ex_index::<F>();
 
-        let callback = ssl.ssl_context()
+        let callback = ssl
+            .ssl_context()
             .ex_data(callback_idx)
             .expect("BUG: psk callback missing") as *const F;
         let identity = if identity != ptr::null() {
@@ -152,16 +153,13 @@ where
     }
 }
 
-pub extern "C" fn raw_sni<F>(ssl: *mut ffi::SSL, al: *mut c_int, _arg: *mut c_void) -> c_int
+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, &mut SslAlert) -> Result<(), SniError> + 'static + Sync + Send,
 {
     unsafe {
         let ssl = SslRef::from_ptr_mut(ssl);
-        let callback = ssl
-            .ssl_context()
-            .ex_data(SslContext::cached_ex_index::<F>())
-            .expect("BUG: sni callback missing") as *const F;
+        let callback = arg as *const F;
         let mut alert = SslAlert(*al);
 
         let r = (*callback)(ssl, &mut alert);
diff --git a/openssl/src/ssl/mod.rs b/openssl/src/ssl/mod.rs
index d38063bc..f3a02c6e 100644
--- a/openssl/src/ssl/mod.rs
+++ b/openssl/src/ssl/mod.rs
@@ -658,7 +658,14 @@ impl SslContextBuilder {
         F: Fn(&mut SslRef, &mut SslAlert) -> Result<(), SniError> + 'static + Sync + Send,
     {
         unsafe {
-            self.set_ex_data(SslContext::cached_ex_index::<F>(), callback);
+            // The SNI callback is somewhat unique in that the callback associated with the original
+            // context associated with an SSL can be used even if the SSL's context has been swapped
+            // out. When that happens, we wouldn't be able to look up the callback's state in the
+            // context's ex data. Instead, pass the pointer directly as the servername arg. It's
+            // still stored in ex data to manage the lifetime.
+            let arg = self.set_ex_data_inner(SslContext::cached_ex_index::<F>(), callback);
+            ffi::SSL_CTX_set_tlsext_servername_arg(self.as_ptr(), arg);
+
             let f: extern "C" fn(_, _, _) -> _ = raw_sni::<F>;
             let f: extern "C" fn() = mem::transmute(f);
             ffi::SSL_CTX_set_tlsext_servername_callback(self.as_ptr(), Some(f));
@@ -1514,13 +1521,14 @@ impl SslContextBuilder {
     ///
     /// [`SSL_CTX_set_ex_data`]: https://www.openssl.org/docs/man1.0.2/ssl/SSL_CTX_set_ex_data.html
     pub fn set_ex_data<T>(&mut self, index: Index<SslContext, T>, data: T) {
+        self.set_ex_data_inner(index, data);
+    }
+
+    fn set_ex_data_inner<T>(&mut self, index: Index<SslContext, T>, data: T) -> *mut c_void {
         unsafe {
-            let data = Box::new(data);
-            ffi::SSL_CTX_set_ex_data(
-                self.as_ptr(),
-                index.as_raw(),
-                Box::into_raw(data) as *mut c_void,
-            );
+            let data = Box::into_raw(Box::new(data)) as *mut c_void;
+            ffi::SSL_CTX_set_ex_data(self.as_ptr(), index.as_raw(), data);
+            data
         }
     }
 
diff --git a/openssl/src/ssl/test.rs b/openssl/src/ssl/test.rs
index 1c44c0b1..e1a6a04b 100644
--- a/openssl/src/ssl/test.rs
+++ b/openssl/src/ssl/test.rs
@@ -29,7 +29,7 @@ use ssl::{
 };
 #[cfg(any(ossl102, ossl110))]
 use x509::verify::X509CheckFlags;
-use x509::{X509Name, X509StoreContext, X509VerifyResult, X509};
+use x509::{X509, X509Name, X509StoreContext, X509VerifyResult};
 
 use std::net::UdpSocket;
 
@@ -1754,3 +1754,42 @@ fn psk_ciphers() {
 
     assert!(CLIENT_CALLED.load(Ordering::SeqCst) && SERVER_CALLED.load(Ordering::SeqCst));
 }
+
+#[test]
+fn sni_callback_swapped_ctx() {
+    static CALLED_BACK: AtomicBool = ATOMIC_BOOL_INIT;
+
+    let listener = TcpListener::bind("127.0.0.1:0").unwrap();
+    let port = listener.local_addr().unwrap().port();
+
+    let guard = thread::spawn(move || {
+        let stream = listener.accept().unwrap().0;
+        let mut ctx = SslContext::builder(SslMethod::tls()).unwrap();
+        ctx.set_servername_callback(|_, _| {
+            CALLED_BACK.store(true, Ordering::SeqCst);
+            Ok(())
+        });
+        let mut ssl = Ssl::new(&ctx.build()).unwrap();
+
+        let mut ctx = SslContext::builder(SslMethod::tls()).unwrap();
+        ctx.set_certificate_file(&Path::new("test/cert.pem"), SslFiletype::PEM)
+            .unwrap();
+        ctx.set_private_key_file(&Path::new("test/key.pem"), SslFiletype::PEM)
+            .unwrap();
+        ssl.set_ssl_context(&ctx.build()).unwrap();
+
+        let mut stream = ssl.accept(stream).unwrap();
+        stream.write_all(&[0]).unwrap();
+    });
+
+    let stream = TcpStream::connect(("127.0.0.1", port)).unwrap();
+    let ctx = SslContext::builder(SslMethod::tls()).unwrap();
+    let ssl = Ssl::new(&ctx.build()).unwrap();
+
+    let mut stream = ssl.connect(stream).unwrap();
+    stream.read_exact(&mut [0]).unwrap();
+
+    assert!(CALLED_BACK.load(Ordering::SeqCst));
+
+    guard.join().unwrap();
+}