diff --git a/.evergreen/scripts/setup-system.sh b/.evergreen/scripts/setup-system.sh
index d8552e0ad2..9158414cce 100755
--- a/.evergreen/scripts/setup-system.sh
+++ b/.evergreen/scripts/setup-system.sh
@@ -38,4 +38,14 @@ if [ "$(uname -s)" = "Darwin" ]; then
     fi
 fi
 
+if [ -w /etc/hosts ]; then
+  SUDO=""
+else
+  SUDO="sudo"
+fi
+
+# Add 'server' and 'hostname_not_in_cert' as a hostnames
+echo "127.0.0.1 server" | $SUDO tee -a /etc/hosts
+echo "127.0.0.1 hostname_not_in_cert" | $SUDO tee -a /etc/hosts
+
 echo "Setting up system... done."
diff --git a/test/asynchronous/test_ssl.py b/test/asynchronous/test_ssl.py
index a05bc9379d..0ce3e8bbac 100644
--- a/test/asynchronous/test_ssl.py
+++ b/test/asynchronous/test_ssl.py
@@ -304,8 +304,13 @@ async def test_cert_ssl_uri_support(self):
         client = self.simple_client(uri_fmt % (CLIENT_PEM, "true", CA_PEM))
         await self.assertClientWorks(client)
 
+    @unittest.skipIf(
+        "PyPy" in sys.version and not _IS_SYNC,
+        "https://github.com/pypy/pypy/issues/5131 flaky on async PyPy due to SSL EOF",
+    )
     @async_client_context.require_tlsCertificateKeyFile
     @async_client_context.require_server_resolvable
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_cert_ssl_validation_hostname_matching(self):
         # Expects the server to be running with server.pem and ca.pem
@@ -430,8 +435,13 @@ async def test_tlsCRLFile_support(self):
                     self.simple_client(uri_fmt % (CRL_PEM, CA_PEM), **self.credentials)  # type: ignore[arg-type]
                 )
 
+    @unittest.skipIf(
+        "PyPy" in sys.version and not _IS_SYNC,
+        "https://github.com/pypy/pypy/issues/5131 flaky on async PyPy due to SSL EOF",
+    )
     @async_client_context.require_tlsCertificateKeyFile
     @async_client_context.require_server_resolvable
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_validation_with_system_ca_certs(self):
         # Expects the server to be running with server.pem and ca.pem.
diff --git a/test/test_ssl.py b/test/test_ssl.py
index 3ac0a4555a..b1e9a65eb5 100644
--- a/test/test_ssl.py
+++ b/test/test_ssl.py
@@ -304,8 +304,13 @@ def test_cert_ssl_uri_support(self):
         client = self.simple_client(uri_fmt % (CLIENT_PEM, "true", CA_PEM))
         self.assertClientWorks(client)
 
+    @unittest.skipIf(
+        "PyPy" in sys.version and not _IS_SYNC,
+        "https://github.com/pypy/pypy/issues/5131 flaky on async PyPy due to SSL EOF",
+    )
     @client_context.require_tlsCertificateKeyFile
     @client_context.require_server_resolvable
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_cert_ssl_validation_hostname_matching(self):
         # Expects the server to be running with server.pem and ca.pem
@@ -430,8 +435,13 @@ def test_tlsCRLFile_support(self):
                     self.simple_client(uri_fmt % (CRL_PEM, CA_PEM), **self.credentials)  # type: ignore[arg-type]
                 )
 
+    @unittest.skipIf(
+        "PyPy" in sys.version and not _IS_SYNC,
+        "https://github.com/pypy/pypy/issues/5131 flaky on async PyPy due to SSL EOF",
+    )
     @client_context.require_tlsCertificateKeyFile
     @client_context.require_server_resolvable
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_validation_with_system_ca_certs(self):
         # Expects the server to be running with server.pem and ca.pem.