diff --git a/cheroot/ssl/builtin.py b/cheroot/ssl/builtin.py
index 1cec20255d..077bb6ecce 100644
--- a/cheroot/ssl/builtin.py
+++ b/cheroot/ssl/builtin.py
@@ -276,7 +276,7 @@ def wrap(self, sock):
         try:
             s = self.context.wrap_socket(
                 sock,
-                do_handshake_on_connect=True,
+                do_handshake_on_connect=False,
                 server_side=True,
             )
         except (
@@ -306,6 +306,97 @@ def wrap(self, sock):
 
         return s, self.get_environ(s)
 
+    def _handle_plain_http_error(self, wfile, buf):
+        try:
+            wfile.write(buf)
+        except OSError as ex:
+            if ex.args[0] not in errors.socket_errors_to_ignore:
+                raise
+
+    def _handle_handshake_failure(self, conn):
+        try:
+            conn.socket.shutdown(socket.SHUT_RDWR)
+        except Exception:
+            # pass
+            return
+
+    def do_handshake(self, conn):
+        """Process SSL handshake on connection if needed.
+
+        Args:
+            conn (:py:class:`~cheroot.server.HTTPConnection`): HTTP connection
+        """
+        ssl_handshake_must_be_done = (
+            conn
+            and getattr(conn, 'socket', None)
+            and getattr(conn.socket, 'do_handshake', None)
+            and not getattr(conn.socket, 'cheroot_handshake_done', False)
+        )
+        if ssl_handshake_must_be_done:
+            conn.socket.cheroot_handshake_done = True
+            do_shutdown = False
+            try:
+                conn.socket.do_handshake()
+            except ssl.SSLError as generic_tls_error:
+                do_shutdown = True
+
+                # Try to send HTTP 400 status for plain text queries
+                peer_speaks_plain_http_over_https = (
+                    generic_tls_error.errno == ssl.SSL_ERROR_SSL
+                    and _assert_ssl_exc_contains(
+                        generic_tls_error,
+                        'http request',
+                    )
+                )
+                if peer_speaks_plain_http_over_https:
+                    msg = (
+                        'The client %s:%s sent a plain HTTP request, but '
+                        'this server only speaks HTTPS on this port.'
+                    )
+                    msg = msg % (conn.remote_addr, conn.remote_port)
+                    buf = [
+                        '%s 400 Bad Request\r\n' % conn.server.protocol,
+                        'Content-Length: %s\r\n' % len(msg),
+                        'Content-Type: text/plain\r\n\r\n',
+                        msg,
+                    ]
+                    conn.server.error_log(msg)
+
+                    # - writing directly on conn.socket attempt to use
+                    #   non-initialized SSL layer and raises exception:
+                    #   EOF occurred in violation of protocol (_ssl.c:2427)
+                    # - conn.socket.unwrap fails raising exception:
+                    #   [SSL: SHUTDOWN_WHILE_IN_INIT] shutdown while in
+                    #   init (_ssl.c:2706)
+                    # - we create a non SSL socket to send plain text reply
+                    conn.socket = socket.socket(fileno=conn.socket.detach())
+                    wfile = StreamWriter(
+                        conn.socket,
+                        'wb',
+                        DEFAULT_BUFFER_SIZE,
+                    )
+                    buf = ''.join(buf).encode('ISO-8859-1')
+                    self._handle_plain_http_error(wfile, buf)
+                else:
+                    msg = 'SSL handshake for %s:%s failed with SSL error:%s'
+                    msg = msg % (
+                        conn.remote_addr,
+                        conn.remote_port,
+                        generic_tls_error,
+                    )
+                    conn.server.error_log(msg)
+
+            except Exception as generic_error:
+                do_shutdown = True
+
+                msg = 'SSL handshake for %s:%s failed with error:%s'
+                msg = msg % (conn.remote_addr, conn.remote_port, generic_error)
+                conn.server.error_log(msg)
+
+            finally:
+                if do_shutdown:
+                    self._handle_handshake_failure(conn)
+
     def get_environ(self, sock):
         """Create WSGI environ entries to be merged into each request."""
         cipher = sock.cipher()
diff --git a/cheroot/ssl/builtin.pyi b/cheroot/ssl/builtin.pyi
index ca106aca12..fcf896dad6 100644
--- a/cheroot/ssl/builtin.pyi
+++ b/cheroot/ssl/builtin.pyi
@@ -20,5 +20,6 @@ class BuiltinSSLAdapter(Adapter):
     def context(self, context) -> None: ...
     def bind(self, sock): ...
     def wrap(self, sock): ...
+    def do_handshake(self, conn) -> None: ...
     def get_environ(self, sock): ...
     def makefile(self, sock, mode: str = ..., bufsize: int = ...): ...
diff --git a/cheroot/workers/threadpool.py b/cheroot/workers/threadpool.py
index a68da6d214..eead5e3e69 100644
--- a/cheroot/workers/threadpool.py
+++ b/cheroot/workers/threadpool.py
@@ -276,7 +276,6 @@ def __init__(
         self._threads = []
         self._queue = queue.Queue(maxsize=accepted_queue_size)
         self._queue_put_timeout = accepted_queue_timeout
-        self.get = self._queue.get
         self._pending_shutdowns = collections.deque()
 
     def start(self):
@@ -294,6 +293,24 @@ def idle(self):  # noqa: D401; irrelevant for properties
         idles = len([t for t in self._threads if t.conn is None])
         return max(idles - len(self._pending_shutdowns), 0)
 
+    def get(self):
+        """Get request from queue, and process SSL handshake is needed.
+
+        Return:
+            conn (:py:class:`~cheroot.server.HTTPConnection`): HTTP connection
+                 ready to be processed
+
+        """
+        conn = self._queue.get()
+        ssl_adapter = self.server.ssl_adapter
+        check_for_ssl_handshake = (
+            ssl_adapter is not None
+            and getattr(ssl_adapter, 'do_handshake', None) is not None
+        )
+        if check_for_ssl_handshake:
+            ssl_adapter.do_handshake(conn)
+        return conn
+
     def put(self, obj):
         """Put request into queue.
 
diff --git a/cheroot/workers/threadpool.pyi b/cheroot/workers/threadpool.pyi
index 02a09b6c90..89c4e7e7a7 100644
--- a/cheroot/workers/threadpool.pyi
+++ b/cheroot/workers/threadpool.pyi
@@ -24,7 +24,6 @@ class ThreadPool:
     server: Any
     min: Any
     max: Any
-    get: Any
     def __init__(
         self,
         server,
@@ -36,6 +35,7 @@ class ThreadPool:
     def start(self) -> None: ...
     @property
     def idle(self): ...
+    def get(self) -> Any: ...
     def put(self, obj) -> None: ...
     def grow(self, amount) -> None: ...
     def shrink(self, amount) -> None: ...