diff --git a/changelogs/fragments/ansible-test-pyopenssl.yaml b/changelogs/fragments/ansible-test-pyopenssl.yaml
index f05ef8ead33..c6d93f3be98 100644
--- a/changelogs/fragments/ansible-test-pyopenssl.yaml
+++ b/changelogs/fragments/ansible-test-pyopenssl.yaml
@@ -1,2 +1,2 @@
-bugfixes:
-  - ansible-test - When installing ``cryptography < 3.4`` also install ``pyopenssl < 22`` to avoid conflicts.
+minor_changes:
+  - ansible-test - Installation of ``cryptography`` is no longer version constrained when ``openssl`` 1.1.0 or later is installed.
diff --git a/test/lib/ansible_test/_internal/python_requirements.py b/test/lib/ansible_test/_internal/python_requirements.py
index 409851fe745..21e59479a3f 100644
--- a/test/lib/ansible_test/_internal/python_requirements.py
+++ b/test/lib/ansible_test/_internal/python_requirements.py
@@ -452,11 +452,11 @@ def get_cryptography_requirements(python):  # type: (PythonConfig) -> t.List[str
         # pyopenssl 20.0.0 requires cryptography 3.2 or later
         pyopenssl = 'pyopenssl < 20.0.0'
     else:
-        # cryptography 3.4+ fails to install on many systems
-        # this is a temporary work-around until a more permanent solution is available
-        cryptography = 'cryptography < 3.4'
-        # pyopenssl 20.0.0 requires cryptography 35 or later
-        pyopenssl = 'pyopenssl < 22.0.0'
+        # cryptography 3.4+ builds require a working rust toolchain
+        # systems bootstrapped using ansible-core-ci can access additional wheels through the spare-tire package index
+        cryptography = 'cryptography'
+        # any future installation of pyopenssl is free to use any compatible version of cryptography
+        pyopenssl = ''
 
     requirements = [
         cryptography,
diff --git a/test/lib/ansible_test/_util/target/setup/bootstrap.sh b/test/lib/ansible_test/_util/target/setup/bootstrap.sh
index 30752f38489..d65a614f339 100644
--- a/test/lib/ansible_test/_util/target/setup/bootstrap.sh
+++ b/test/lib/ansible_test/_util/target/setup/bootstrap.sh
@@ -145,6 +145,13 @@ bootstrap_remote_freebsd()
         sed -i '' 's/^# *PermitRootLogin.*$/PermitRootLogin yes/;' /etc/ssh/sshd_config
         service sshd restart
     fi
+
+    # make additional wheels available for packages which lack them for this platform
+    echo "# generated by ansible-test
+[global]
+extra-index-url = https://spare-tire.testing.ansible.com/simple/
+prefer-binary = yes
+" > /etc/pip.conf
 }
 
 bootstrap_remote_macos()