diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 112719c0..8e2920c0 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -24,43 +24,35 @@ jobs:
             python-version: "3.10"
             tox-env: py310
           - name: py2.7
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: py27
           - name: py2.7 with old gmpy
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: py27_old_gmpy
           - name: py2.7 with old gmpy2
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: py27_old_gmpy2
           - name: py2.7 with old six
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: py27_old_six
           - name: py2.7 with gmpy
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: gmpypy27
           - name: py2.7 with gmpy2
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             tox-env: gmpy2py27
-          - name: py3.3
-            os: ubuntu-18.04
-            python-version: 3.3
-            tox-env: py33
-          - name: py3.4
-            os: ubuntu-18.04
-            python-version: 3.4
-            tox-env: py34
           - name: py3.5
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 3.5
             tox-env: py35
           - name: py3.6
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 3.6
             tox-env: py36
           - name: py3.7
@@ -89,8 +81,12 @@ jobs:
             tox-env: gmpy2py310
           - name: py3.11
             os: ubuntu-latest
-            python-version: '3.11.0-beta.3'
+            python-version: '3.11'
             tox-env: py311
+          - name: py3.12
+            os: ubuntu-latest
+            python-version: '3.12.0-alpha.5'
+            tox-env: py312
           - name: pypy
             os: ubuntu-latest
             python-version: pypy-2.7
@@ -101,7 +97,7 @@ jobs:
             tox-env: pypy3
           # special configurations
           - name: py2.7 with instrumental
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             python-version: 2.7
             opt-deps: ['instrumental']
           - name: code checks
diff --git a/README.md b/README.md
index 11a00160..7cffeb17 100644
--- a/README.md
+++ b/README.md
@@ -45,7 +45,7 @@ curves over prime fields.
 ## Dependencies
 
 This library uses only Python and the 'six' package. It is compatible with
-Python 2.6, 2.7, and 3.3+. It also supports execution on alternative
+Python 2.6, 2.7, and 3.5+. It also supports execution on alternative
 implementations like pypy and pypy3.
 
 If `gmpy2` or `gmpy` is installed, they will be used for faster arithmetic.
diff --git a/build-requirements-3.3.txt b/build-requirements-3.3.txt
deleted file mode 100644
index d817d2b3..00000000
--- a/build-requirements-3.3.txt
+++ /dev/null
@@ -1,9 +0,0 @@
-git+https://github.com/tomato42/coveralls-python.git@add-py26#egg=coveralls
-pluggy<0.6
-tox<3
-wheel<0.30
-virtualenv==15.2.0
-enum34
-hypothesis<3.44
-coverage<5.0
-urllib3<=1.25.8
diff --git a/build-requirements-3.4.txt b/build-requirements-3.4.txt
deleted file mode 100644
index ee734d11..00000000
--- a/build-requirements-3.4.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-tox
-git+https://github.com/tomato42/coveralls-python.git@add-py26#egg=coveralls
-hypothesis
-pytest>=4.6.0
-PyYAML<5.3
-coverage
-attrs<21
diff --git a/setup.py b/setup.py
index f6a1dd1e..a9ae2439 100755
--- a/setup.py
+++ b/setup.py
@@ -27,15 +27,13 @@
     package_dir={"": "src"},
     license="MIT",
     cmdclass=commands,
-    python_requires=">=2.6, !=3.0.*, !=3.1.*, !=3.2.*",
+    python_requires=">=2.6, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*",
     classifiers=[
         "Programming Language :: Python",
         "Programming Language :: Python :: 2",
         "Programming Language :: Python :: 2.6",
         "Programming Language :: Python :: 2.7",
         "Programming Language :: Python :: 3",
-        "Programming Language :: Python :: 3.3",
-        "Programming Language :: Python :: 3.4",
         "Programming Language :: Python :: 3.5",
         "Programming Language :: Python :: 3.6",
         "Programming Language :: Python :: 3.7",
@@ -43,6 +41,7 @@
         "Programming Language :: Python :: 3.9",
         "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: 3.11",
+        "Programming Language :: Python :: 3.12",
     ],
     install_requires=["six>=1.9.0"],
     extras_require={"gmpy2": "gmpy2", "gmpy": "gmpy"},
diff --git a/src/ecdsa/_compat.py b/src/ecdsa/_compat.py
index 83d41a5f..f409a1a2 100644
--- a/src/ecdsa/_compat.py
+++ b/src/ecdsa/_compat.py
@@ -91,28 +91,13 @@ def int_to_bytes(val, length=None, byteorder="big"):
         raise ValueError("Only 'big' or 'little' endian supported")
 
 else:
-    if sys.version_info < (3, 4):  # pragma: no branch
-        # on python 3.3 hmac.hmac.update() accepts only bytes, on newer
-        # versions it does accept memoryview() also
-        def hmac_compat(data):
-            if not isinstance(data, bytes):  # pragma: no branch
-                return bytes(data)
-            return data
-
-        def normalise_bytes(buffer_object):
-            """Cast the input into array of bytes."""
-            if not buffer_object:
-                return b""
-            return memoryview(buffer_object).cast("B")
 
-    else:
-
-        def hmac_compat(data):
-            return data
+    def hmac_compat(data):
+        return data
 
-        def normalise_bytes(buffer_object):
-            """Cast the input into array of bytes."""
-            return memoryview(buffer_object).cast("B")
+    def normalise_bytes(buffer_object):
+        """Cast the input into array of bytes."""
+        return memoryview(buffer_object).cast("B")
 
     def compat26_str(val):
         return val
diff --git a/src/ecdsa/test_der.py b/src/ecdsa/test_der.py
index 0ca5bd7f..833d12d8 100644
--- a/src/ecdsa/test_der.py
+++ b/src/ecdsa/test_der.py
@@ -144,26 +144,22 @@ def test_old_call_convention(self):
 
     def test_new_call_convention(self):
         """This is how it should be called now."""
-        warnings.simplefilter("always")
-        with pytest.warns(None) as warns:
+        # make sure no warnings are raised
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
             der = encode_bitstring(b"\xff", 0)
 
-        # verify that new call convention doesn't raise Warnings
-        self.assertEqual(len(warns), 0)
-
         self.assertEqual(der, b"\x03\x02\x00\xff")
 
     def test_implicit_unused_bits(self):
         """
         Writing bit string with already included the number of unused bits.
         """
-        warnings.simplefilter("always")
-        with pytest.warns(None) as warns:
+        # make sure no warnings are raised
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
             der = encode_bitstring(b"\x00\xff", None)
 
-        # verify that new call convention doesn't raise Warnings
-        self.assertEqual(len(warns), 0)
-
         self.assertEqual(der, b"\x03\x02\x00\xff")
 
     def test_explicit_unused_bits(self):
@@ -203,22 +199,20 @@ def test_old_call_convention(self):
         self.assertEqual(rest, b"")
 
     def test_new_call_convention(self):
-        warnings.simplefilter("always")
-        with pytest.warns(None) as warns:
+        # make sure no warnings are raised
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
             bits, rest = remove_bitstring(b"\x03\x02\x00\xff", 0)
 
-        self.assertEqual(len(warns), 0)
-
         self.assertEqual(bits, b"\xff")
         self.assertEqual(rest, b"")
 
     def test_implicit_unexpected_unused(self):
-        warnings.simplefilter("always")
-        with pytest.warns(None) as warns:
+        # make sure no warnings are raised
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
             bits, rest = remove_bitstring(b"\x03\x02\x00\xff", None)
 
-        self.assertEqual(len(warns), 0)
-
         self.assertEqual(bits, (b"\xff", 0))
         self.assertEqual(rest, b"")
 
diff --git a/src/ecdsa/test_jacobi.py b/src/ecdsa/test_jacobi.py
index 71fb33e5..322b568c 100644
--- a/src/ecdsa/test_jacobi.py
+++ b/src/ecdsa/test_jacobi.py
@@ -50,7 +50,7 @@ def test_add_with_different_curves(self):
         p_a = PointJacobi.from_affine(generator_256)
         p_b = PointJacobi.from_affine(generator_224)
 
-        with self.assertRaises(ValueError):
+        with self.assertRaises(ValueError):  # pragma: no branch
             p_a + p_b
 
     def test_compare_different_curves(self):
@@ -558,8 +558,12 @@ def test_pickle(self):
         self.assertEqual(pickle.loads(pickle.dumps(pj)), pj)
 
     @settings(**NO_OLD_SETTINGS)
+    @pytest.mark.skipif(
+        platform.python_implementation() == "PyPy",
+        reason="threading on PyPy breaks coverage",
+    )
     @given(st.integers(min_value=1, max_value=10))
-    def test_multithreading(self, thread_num):
+    def test_multithreading(self, thread_num):  # pragma: no cover
         # ensure that generator's precomputation table is filled
         generator_112r2 * 2
 
@@ -592,10 +596,12 @@ def runner(generator):
         )
 
     @pytest.mark.skipif(
-        platform.system() == "Windows",
-        reason="there are no signals on Windows",
+        platform.system() == "Windows"
+        or platform.python_implementation() == "PyPy",
+        reason="there are no signals on Windows, and threading breaks coverage"
+        " on PyPy",
     )
-    def test_multithreading_with_interrupts(self):
+    def test_multithreading_with_interrupts(self):  # pragma: no cover
         thread_num = 10
         # ensure that generator's precomputation table is filled
         generator_112r2 * 2
diff --git a/src/ecdsa/test_numbertheory.py b/src/ecdsa/test_numbertheory.py
index 8bc787f1..239eaa8c 100644
--- a/src/ecdsa/test_numbertheory.py
+++ b/src/ecdsa/test_numbertheory.py
@@ -182,7 +182,7 @@ def st_comp_with_com_fac(draw):
     # select at most 20 lists (returned numbers),
     # each having at most 30 primes (factors) including none (then the number
     # will be 1)
-    comp_primes = draw(
+    comp_primes = draw(  # pragma: no branch
         st.integers(min_value=1, max_value=20).flatmap(
             lambda n: st.lists(
                 st.lists(st.sampled_from(primes), max_size=30),
@@ -225,7 +225,7 @@ def st_comp_no_com_fac(draw):
 
     # select at most 20 lists, each having at most 30 primes
     # selected from the leftover_primes list
-    number_primes = draw(
+    number_primes = draw(  # pragma: no branch
         st.integers(min_value=1, max_value=20).flatmap(
             lambda n: st.lists(
                 st.lists(st.sampled_from(leftover_primes), max_size=30),
diff --git a/src/ecdsa/test_pyecdsa.py b/src/ecdsa/test_pyecdsa.py
index d61f5083..59c876cc 100644
--- a/src/ecdsa/test_pyecdsa.py
+++ b/src/ecdsa/test_pyecdsa.py
@@ -1359,12 +1359,12 @@ def do_test_to_openssl(self, curve, hash_name="SHA1"):
     OPENSSL_SUPPORTED_TYPES = set()
     try:
         if "-rawin" in run_openssl("pkeyutl -help"):
-            OPENSSL_SUPPORTED_TYPES = set(
+            OPENSSL_SUPPORTED_TYPES = set(  # pragma: no branch
                 c.lower()
                 for c in ("ED25519", "ED448")
                 if c in run_openssl("list -public-key-methods")
             )
-    except SubprocessError:
+    except SubprocessError:  # pragma: no cover
         pass
 
     def do_eddsa_test_to_openssl(self, curve):
diff --git a/tox.ini b/tox.ini
index 46864866..c9b07c9a 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,22 +1,17 @@
 
 [tox]
-envlist = py26, py27, py33, py34, py35, py36, py37, py38, py39, py310, py311, py, pypy, pypy3, gmpy2py27, gmpy2py39, gmpy2py310, gmpypy27, gmpypy39, gmpypy310, codechecks
+envlist = py26, py27, py35, py36, py37, py38, py39, py310, py311, py312, py, pypy, pypy3, gmpy2py27, gmpy2py39, gmpy2py310, gmpypy27, gmpypy39, gmpypy310, codechecks
 
 [testenv]
 deps =
-     py{33}: py<1.5
-     py{33}: pytest<3.3
-     py{33}: enum34
-     py{33}: hypothesis<3.44
      py{26}: unittest2
      py{26}: hypothesis<3
-     py{34}: attrs<21
-     py{26,27,34,35,36,37,38,39,310,311,py,py3}: pytest
-     py{27,34,35,36,37,38,39,310,311,py,py3}: hypothesis
-     gmpy2py{27,39,310,311}: gmpy2
-     gmpypy{27,39,310,311}: gmpy
-     gmpy{2py27,2py39,2py310,2py311,py27,py39,py310,py311}: pytest
-     gmpy{2py27,2py39,2py310,2py311,py27,py39,py310,py311}: hypothesis
+     py{26,27,35,36,37,38,39,310,311,312,py,py3}: pytest
+     py{27,35,36,37,38,39,310,311,312,py,py3}: hypothesis
+     gmpy2py{27,39,310,311,312}: gmpy2
+     gmpypy{27,39,310,311,312}: gmpy
+     gmpy{2py27,2py39,2py310,2py311,2py312,py27,py39,py310,py311,py312}: pytest
+     gmpy{2py27,2py39,2py310,2py311,2py312,py27,py39,py310,py311,py312}: hypothesis
 # six==1.9.0 comes from setup.py install_requires
      py27_old_six: six==1.9.0
      py27_old_six: pytest
@@ -31,7 +26,6 @@ deps =
      py27_old_gmpy2: hypothesis
      py: pytest
      py: hypothesis
-     py{33}: wheel<0.30
      coverage
 commands = coverage run --branch -m pytest {posargs:src/ecdsa}
 
@@ -56,6 +50,9 @@ basepython=python3.10
 [testenv:gmpypy311]
 basepython=python3.11
 
+[testenv:gmpypy312]
+basepython=python3.12
+
 [testenv:gmpy2py27]
 basepython=python2.7
 
@@ -68,6 +65,9 @@ basepython=python3.10
 [testenv:gmpy2py311]
 basepython=python3.11
 
+[testenv:gmpy2py312]
+basepython=python3.12
+
 [testenv:instrumental]
 basepython = python2.7
 deps =