diff --git a/scrapy/core/downloader/contextfactory.py b/scrapy/core/downloader/contextfactory.py
index 4abde2238..bc6ad34d8 100644
--- a/scrapy/core/downloader/contextfactory.py
+++ b/scrapy/core/downloader/contextfactory.py
@@ -61,7 +61,9 @@ class ScrapyClientContextFactory(BrowserLikePolicyForHTTPS):
     # kept for old-style HTTP/1.0 downloader context twisted calls,
     # e.g. connectSSL()
     def getContext(self, hostname=None, port=None):
-        return self.getCertificateOptions().getContext()
+        ctx = self.getCertificateOptions().getContext()
+        ctx.set_options(0x4)  # OP_LEGACY_SERVER_CONNECT
+        return ctx
 
     def creatorForNetloc(self, hostname, port):
         return ScrapyClientTLSOptions(hostname.decode("ascii"), self.getContext(),
diff --git a/scrapy/core/downloader/tls.py b/scrapy/core/downloader/tls.py
index 7d67a426f..65028d21f 100644
--- a/scrapy/core/downloader/tls.py
+++ b/scrapy/core/downloader/tls.py
@@ -17,10 +17,10 @@ METHOD_TLSv12 = 'TLSv1.2'
 
 
 openssl_methods = {
-    METHOD_TLS: SSL.SSLv23_METHOD,                      # protocol negotiation (recommended)
-    METHOD_TLSv10: SSL.TLSv1_METHOD,                    # TLS 1.0 only
-    METHOD_TLSv11: getattr(SSL, 'TLSv1_1_METHOD', 5),   # TLS 1.1 only
-    METHOD_TLSv12: getattr(SSL, 'TLSv1_2_METHOD', 6),   # TLS 1.2 only
+    METHOD_TLS: SSL.SSLv23_METHOD,      # protocol negotiation (recommended)
+    METHOD_TLSv10: SSL.TLSv1_METHOD,    # TLS 1.0 only
+    METHOD_TLSv11: SSL.TLSv1_1_METHOD,  # TLS 1.1 only
+    METHOD_TLSv12: SSL.TLSv1_2_METHOD,  # TLS 1.2 only
 }
 
 
diff --git a/scrapy/utils/ssl.py b/scrapy/utils/ssl.py
index ea4dde882..ce211bf9b 100644
--- a/scrapy/utils/ssl.py
+++ b/scrapy/utils/ssl.py
@@ -1,14 +1,9 @@
-import OpenSSL
+import OpenSSL.SSL
 import OpenSSL._util as pyOpenSSLutil
 
 from scrapy.utils.python import to_unicode
 
 
-# The OpenSSL symbol is present since 1.1.1 but it's not currently supported in any version of pyOpenSSL.
-# Using the binding directly, as this code does, requires cryptography 2.4.
-SSL_OP_NO_TLSv1_3 = getattr(pyOpenSSLutil.lib, 'SSL_OP_NO_TLSv1_3', 0)
-
-
 def ffi_buf_to_string(buf):
     return to_unicode(pyOpenSSLutil.ffi.string(buf))
 
@@ -22,9 +17,6 @@ def x509name_to_string(x509name):
 
 
 def get_temp_key_info(ssl_object):
-    if not hasattr(pyOpenSSLutil.lib, 'SSL_get_server_tmp_key'):  # requires OpenSSL 1.0.2
-        return None
-
     # adapted from OpenSSL apps/s_cb.c::ssl_print_tmp_key()
     temp_key_p = pyOpenSSLutil.ffi.new("EVP_PKEY **")
     if not pyOpenSSLutil.lib.SSL_get_server_tmp_key(ssl_object, temp_key_p):
diff --git a/tests/mockserver.py b/tests/mockserver.py
index 6d2d95692..4fd3adce7 100644
--- a/tests/mockserver.py
+++ b/tests/mockserver.py
@@ -19,7 +19,6 @@ from twisted.web.static import File
 from twisted.web.util import redirectTo
 
 from scrapy.utils.python import to_bytes, to_unicode
-from scrapy.utils.ssl import SSL_OP_NO_TLSv1_3
 from scrapy.utils.test import get_testenv
 
 
@@ -350,7 +349,7 @@ def ssl_context_factory(keyfile='keys/localhost.key', certfile='keys/localhost.c
     if cipher_string:
         ctx = factory.getContext()
         # disabling TLS1.3 because it unconditionally enables some strong ciphers
-        ctx.set_options(SSL.OP_CIPHER_SERVER_PREFERENCE | SSL_OP_NO_TLSv1_3)
+        ctx.set_options(SSL.OP_CIPHER_SERVER_PREFERENCE | SSL.OP_NO_TLSv1_3)
         ctx.set_cipher_list(to_bytes(cipher_string))
     return factory