diff --git a/.github/actions/setup-python/action.yml b/.github/actions/setup-python/action.yml
index dd5094e9d3..1a761225b4 100644
--- a/.github/actions/setup-python/action.yml
+++ b/.github/actions/setup-python/action.yml
@@ -15,8 +15,10 @@ runs:
         # `requires_python` and `marker_python_version`. For all other versions, we let
         # the GitHub runner pick a micro version, which will be faster because it's
         # locally cached.
+        #
+        # When updating this list, see the comment in ci.yml about integration test
+        # runner versions.
         python-version: |
-          3.6
           3.7
           3.8.10
           3.9
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 0daaec2b33..51442e18e3 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -14,7 +14,7 @@ defaults:
 jobs:
 
   product:
-    runs-on: ubuntu-20.04
+    runs-on: ubuntu-22.04
     steps:
       - uses: smorimoto/tune-github-hosted-runner-network@v1.0.0
       - uses: actions/checkout@v4.1.6
@@ -72,7 +72,7 @@ jobs:
 
 
   docs:
-    runs-on: ubuntu-20.04
+    runs-on: ubuntu-22.04
     steps:
       - uses: smorimoto/tune-github-hosted-runner-network@v1.0.0
       - uses: actions/checkout@v4.1.6
@@ -103,7 +103,7 @@ jobs:
 
 
   gradlePython:
-    runs-on: ubuntu-20.04
+    runs-on: ubuntu-22.04
     steps:
       - uses: smorimoto/tune-github-hosted-runner-network@v1.0.0
       - uses: actions/checkout@v4.1.6
@@ -120,7 +120,7 @@ jobs:
 
   demo:
     needs: [product]
-    runs-on: ubuntu-20.04
+    runs-on: ubuntu-22.04
     steps:
       - uses: smorimoto/tune-github-hosted-runner-network@v1.0.0
       - uses: actions/checkout@v4.1.6
@@ -160,12 +160,12 @@ jobs:
         agp-version: ${{ fromJSON(needs.product.outputs.agp-versions) }}
         os: [linux, macos, windows]
         include:
-          # To avoid clutter in the GitHub UI, OS versions are not added to the `os`
-          # dimension directly.
+          # Runners must support all the Python versions in setup-python/action.yml: see
+          # https://github.com/actions/python-versions/blob/main/versions-manifest.json.
           - os: linux
-            runs-on: ubuntu-20.04  # 22.04 has a minimum Python version of 3.7 (see setup-python)
+            runs-on: ubuntu-22.04
           - os: macos
-            runs-on: macos-12  # 14 has a minimum Python version of 3.8 (see setup-python)
+            runs-on: macos-12
           - os: windows
             runs-on: windows-2022
 
diff --git a/product/gradle-plugin/README.md b/product/gradle-plugin/README.md
index 3b57144637..48750f44a1 100644
--- a/product/gradle-plugin/README.md
+++ b/product/gradle-plugin/README.md
@@ -105,10 +105,12 @@ After stable release:
 
 * Increment Chaquopy major version if not already done.
 * Update gradle-plugin/src/main/python/chaquopy/util.py.
-* Update `testPython` in gradle-plugin/build.gradle, and run the tests.
 * In test_gradle_plugin, update `OLD_BUILD_PYTHON_VERSION` and
   `MIN_BUILD_PYTHON_VERSION`, and run the tests which use them.
+* Run `gradle:testPython`.
 * Update the list of Python versions in .github/actions/setup-python/action.yml.
+* See the comment in ci.yml about integration test runner versions, and consider
+  updating them.
 * Update android.rst.
 
 
diff --git a/product/gradle-plugin/build.gradle.kts b/product/gradle-plugin/build.gradle.kts
index 3a2cb742c0..b0bffc00b3 100644
--- a/product/gradle-plugin/build.gradle.kts
+++ b/product/gradle-plugin/build.gradle.kts
@@ -133,17 +133,41 @@ abstract class TestPythonTask : DefaultTask() {
     }
 }
 
-tasks.register<TestPythonTask>("testPython") {
-    pythonVersion = "3.7"  // Minimum supported buildPython version
-    workingDir = "$projectDir/src/test/python"
-}
 
-tasks.register("testIntegration") {
+tasks.register("testPython") {
     group = "verification"
+}.let {
+    tasks.named("check") { dependsOn(it) }
+}
+
+var minPythonMinor: Int? = null
+var maxPythonMinor: Int? = null
+file("src/test/integration/test_gradle_plugin.py").useLines {
+    for (line in it) {
+        """MIN_BUILD_PYTHON_VERSION = "3.(\d+)""".toRegex().find(line)?.let {
+            minPythonMinor = it.groupValues[1].toInt()
+        }
+        """MAX_BUILD_PYTHON_VERSION = "3.(\d+)""".toRegex().find(line)?.let {
+            maxPythonMinor = it.groupValues[1].toInt()
+        }
+    }
 }
 
-tasks.check {
-    dependsOn("testPython", "testIntegration")
+for (pythonMinor in minPythonMinor!! .. maxPythonMinor!!) {
+    val pythonVer = "3.$pythonMinor"
+    tasks.register<TestPythonTask>("testPython-$pythonVer") {
+        pythonVersion = pythonVer
+        workingDir = "$projectDir/src/test/python"
+    }.let {
+        tasks.named("testPython") { dependsOn(it) }
+    }
+}
+
+
+tasks.register("testIntegration") {
+    group = "verification"
+}.let {
+    tasks.named("check") { dependsOn(it) }
 }
 
 // This should match the version discovery logic in ci.yml.
@@ -151,7 +175,7 @@ val INTEGRATION_DIR = "$projectDir/src/test/integration"
 for (f in file("$INTEGRATION_DIR/data/base").listFiles()!!) {
     val version = f.name
     if (version.contains(".")) {
-        val task = tasks.register<TestPythonTask>("testIntegration-$version") {
+        tasks.register<TestPythonTask>("testIntegration-$version") {
             pythonVersion = Common.DEFAULT_PYTHON_VERSION
             if (System.getenv("CHAQUOPY_NO_BUILD") == null) {  // Used in CI
                 dependsOn(tasks.publish, ":runtime:publish")
@@ -159,7 +183,8 @@ for (f in file("$INTEGRATION_DIR/data/base").listFiles()!!) {
             workingDir = INTEGRATION_DIR
             environment["CHAQUOPY_AGP_VERSION"] = version
             environment["ANDROID_HOME"] = BuildCommon.androidHome(project)
+        }.let {
+            tasks.named("testIntegration") { dependsOn(it) }
         }
-        tasks.named("testIntegration") { dependsOn(task) }
     }
 }
diff --git a/product/gradle-plugin/src/main/python/chaquopy/static_proxy.py b/product/gradle-plugin/src/main/python/chaquopy/static_proxy.py
index 908c871b9e..56c995404c 100644
--- a/product/gradle-plugin/src/main/python/chaquopy/static_proxy.py
+++ b/product/gradle-plugin/src/main/python/chaquopy/static_proxy.py
@@ -15,7 +15,6 @@
 from os.path import exists, isdir, isfile
 import sys
 import tokenize
-import warnings
 
 import attr
 from attr.validators import instance_of, optional
@@ -41,10 +40,6 @@ def unwrap_if_primitive(name):
 
 
 def main():
-    # TODO: remove once our minimum buildPython version is Python 3.8.
-    for message in [r".*use ast.Constant instead", r".*use value instead"]:
-        warnings.filterwarnings("ignore", message, DeprecationWarning)
-
     args = parse_args()
 
     try:
@@ -296,11 +291,7 @@ def has_kwargs(self, call):
             return any(kw.arg is None for kw in call.keywords)
 
     def evaluate(self, expr):
-        if isinstance(expr, ast.Num):
-            return expr.n
-        elif isinstance(expr, ast.Str):
-            return expr.s
-        elif isinstance(expr, ast.NameConstant):  # True, False, None
+        if isinstance(expr, ast.Constant):
             return expr.value
         elif isinstance(expr, ast.Name):
             return self.resolve(expr)
diff --git a/product/gradle-plugin/src/main/python/chaquopy/util.py b/product/gradle-plugin/src/main/python/chaquopy/util.py
index 84128ed44f..2d00a5e952 100644
--- a/product/gradle-plugin/src/main/python/chaquopy/util.py
+++ b/product/gradle-plugin/src/main/python/chaquopy/util.py
@@ -2,7 +2,7 @@
 
 
 def check_build_python():
-    MIN_VERSION = (3, 7)
+    MIN_VERSION = (3, 8)
     if sys.version_info < MIN_VERSION:
         print("buildPython must be version {}.{} or later: this is version {}.{}.{}. See "
               "https://chaquo.com/chaquopy/doc/current/android.html#buildpython."
diff --git a/product/gradle-plugin/src/test/integration/data/PythonReqs/buildpython/app/build.gradle b/product/gradle-plugin/src/test/integration/data/PythonReqs/buildpython/app/build.gradle
index c98e5238e4..743feb57b7 100644
--- a/product/gradle-plugin/src/test/integration/data/PythonReqs/buildpython/app/build.gradle
+++ b/product/gradle-plugin/src/test/integration/data/PythonReqs/buildpython/app/build.gradle
@@ -20,6 +20,9 @@ android {
                 install "no_binary==1.0"  // sdist
                 install "six==1.16.0"  // PyPI download
             }
+            pyc {
+                pip false
+            }
         }
         ndk {
             abiFilters "x86"
diff --git a/product/gradle-plugin/src/test/integration/data/StaticProxy/buildpython/app/build.gradle b/product/gradle-plugin/src/test/integration/data/StaticProxy/buildpython/app/build.gradle
index 36787f32fa..3c5fd9d2fa 100644
--- a/product/gradle-plugin/src/test/integration/data/StaticProxy/buildpython/app/build.gradle
+++ b/product/gradle-plugin/src/test/integration/data/StaticProxy/buildpython/app/build.gradle
@@ -15,6 +15,9 @@ android {
             buildPython (System.getProperty("os.name").startsWith("Windows") ?
                          "py -$version" : "python$version")
             staticProxy "chaquopy_test.a"
+            pyc {
+                src false
+            }
         }
         ndk {
             abiFilters "x86"
diff --git a/product/gradle-plugin/src/test/integration/test_gradle_plugin.py b/product/gradle-plugin/src/test/integration/test_gradle_plugin.py
index 9588c7c052..d0cca500fa 100644
--- a/product/gradle-plugin/src/test/integration/test_gradle_plugin.py
+++ b/product/gradle-plugin/src/test/integration/test_gradle_plugin.py
@@ -66,8 +66,8 @@ def list_versions(mode):
 BUILD_PYTHON_VERSION = BUILD_PYTHON_VERSION_FULL.rpartition(".")[0]
 
 # When updating these, consider also updating .github/actions/setup-python/action.yml.
-OLD_BUILD_PYTHON_VERSION = "3.6"
-MIN_BUILD_PYTHON_VERSION = "3.7"
+OLD_BUILD_PYTHON_VERSION = "3.7"
+MIN_BUILD_PYTHON_VERSION = "3.8"
 MAX_BUILD_PYTHON_VERSION = "3.12"
 
 EGG_INFO_SUFFIX = "py" + BUILD_PYTHON_VERSION + ".egg-info"
diff --git a/product/gradle-plugin/src/test/python/static_proxy/test_static_proxy.py b/product/gradle-plugin/src/test/python/static_proxy/test_static_proxy.py
index 85a8affc4a..48f2d558b1 100644
--- a/product/gradle-plugin/src/test/python/static_proxy/test_static_proxy.py
+++ b/product/gradle-plugin/src/test/python/static_proxy/test_static_proxy.py
@@ -43,9 +43,10 @@ def test_errors(self):
         for name in ["empty", "no_proxies", "conditional"]:
             self.run_json("errors", name, False, name + ".py: no static_proxy classes found")
 
-        self.run_json("errors", "syntax", False, "syntax.py:3:7: invalid syntax")
+        self.run_json("errors", "syntax", False, "syntax.py:3:5: invalid syntax")
         self.run_json("errors", "syntax_py2", False,
-                      "syntax_py2.py:1:13: Missing parentheses in call to 'print'")
+                      f"syntax_py2.py:1:{7 if sys.version_info < (3, 10) else 1}"
+                      f": Missing parentheses in call to 'print'")
 
         for name in ["starargs", "kwargs"]:
             self.run_json("errors", name, False,
@@ -129,6 +130,9 @@ def run_json(self, path, modules, succeed=True, expected=None, **kwargs):
         if status == 0:
             if not succeed:
                 self.dump_run("run unexpectedly succeeded", stdout, stderr)
+            if stderr:
+                # Probably a DeprecationWarning or similar.
+                self.dump_run("succeeded but wrote to stderr", stdout, stderr)
             try:
                 actual = json.loads(stdout)
             except ValueError:
@@ -150,7 +154,7 @@ def dump_run(self, msg, stdout, stderr):
     def assertInLong(self, a, b, re=False):
         try:
             if re:
-                self.assertRegexpMatches(b, a)
+                self.assertRegex(b, a)
             else:
                 self.assertIn(a, b)
         except AssertionError:
diff --git a/product/gradle-plugin/src/test/python/static_proxy/test_utils.py b/product/gradle-plugin/src/test/python/static_proxy/test_utils.py
index ae76309126..a94a64536f 100644
--- a/product/gradle-plugin/src/test/python/static_proxy/test_utils.py
+++ b/product/gradle-plugin/src/test/python/static_proxy/test_utils.py
@@ -9,7 +9,6 @@ def setUp(self):
         self.cw = catch_warnings()
         self.cw.__enter__()
         filterwarnings("error")
-        filterwarnings("ignore", r"Please use assert\w+ instead")
 
     def tearDown(self):
         self.cw.__exit__(None, None, None)
diff --git a/product/runtime/docs/sphinx/android.rst b/product/runtime/docs/sphinx/android.rst
index f4a94c6472..0bc8781732 100644
--- a/product/runtime/docs/sphinx/android.rst
+++ b/product/runtime/docs/sphinx/android.rst
@@ -167,8 +167,8 @@ example, here's how to create flavors for different :ref:`Python versions
 buildPython
 -----------
 
-Some features require Python 3.7 or later to be available on the build machine. These features
-are indicated by a note in their documentation sections.
+Some features require Python 3.8 or later to be available on the build machine. These
+features are indicated by a note in their documentation sections.
 
 By default, Chaquopy will try to find Python on the PATH with the standard command for your
 operating system, first with a matching minor version, and then with a matching major version.