diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 54bddb46b3..c6247caa1f 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -2,7 +2,7 @@ default_language_version:
   python: python3
 repos:
 - repo: https://github.com/pre-commit/pre-commit-hooks
-  rev: v3.1.0
+  rev: v3.2.0
   hooks:
   - id: check-ast
   - id: check-builtin-literals
@@ -15,33 +15,24 @@ repos:
     exclude: 'tests/test-data'
   - id: trailing-whitespace
     exclude: 'tests/test-data'
-  - id: end-of-file-fixer
-    exclude: 'tests/test-data'
 - repo: https://github.com/asottile/pyupgrade
   rev: v2.7.2
   hooks:
   - id: pyupgrade
-- repo: https://github.com/asottile/seed-isort-config
-  rev: v2.2.0
-  hooks:
-  - id: seed-isort-config
-    args:
-      - --application-directories
-      - .:sourmash
-- repo: https://github.com/timothycrosley/isort
-  rev: 5.3.0
+- repo: https://github.com/pre-commit/mirrors-isort
+  rev: v5.4.2
   hooks:
   - id: isort
     additional_dependencies: [toml]
 - repo: https://github.com/psf/black
-  rev: 19.10b0
+  rev: 20.8b1
   hooks:
   - id: black
     args:
     - --safe
     language_version: python3.8
 - repo: https://github.com/asottile/blacken-docs
-  rev: v1.7.0
+  rev: v1.8.0
   hooks:
   - id: blacken-docs
     additional_dependencies:
@@ -52,7 +43,7 @@ repos:
   hooks:
   - id: add-trailing-comma
 - repo: https://github.com/pre-commit/pygrep-hooks
-  rev: v1.5.1
+  rev: v1.6.0
   hooks:
   - id: rst-backticks
 #- repo: https://github.com/asottile/setup-cfg-fmt
@@ -61,11 +52,11 @@ repos:
 #  - id: setup-cfg-fmt
 #    args:
 #    - --min-py3-version
-#    - '3.5'
-- repo: https://gitlab.com/pycqa/flake8
-  rev: 3.8.3
-  hooks:
-  - id: flake8
-    additional_dependencies:
-    - flake8-bugbear == 20.1.2
-    language_version: python3.8
+#    - '3.7'
+#- repo: https://gitlab.com/pycqa/flake8
+#  rev: 3.8.3
+#  hooks:
+#  - id: flake8
+#    additional_dependencies:
+#    - flake8-bugbear == 20.1.2
+#    language_version: python3.8
diff --git a/tox.ini b/tox.ini
index deaf1e0843..1dcb86030f 100644
--- a/tox.ini
+++ b/tox.ini
@@ -5,6 +5,7 @@ envlist =
   docs,
   package_description
   py37,
+  py39,
 #  fix_lint,
 minversion = 3.12
 isolated_build = true
@@ -44,17 +45,19 @@ commands = pytest \
            --junitxml {toxworkdir}/junit.{envname}.xml \
            {posargs}
 
+[testenv:pypy]
+deps =
+  pip >= 19.3.1
+  psutil <= 5.6.7
+
 [testenv:py38]
 extras =
   test
   storage
 
-[tox:.package]
-basepython = python3
-
 [testenv:docs]
 description = invoke sphinx-build to build the HTML docs
-basepython = python3.7
+basepython = python3.8
 extras = doc
 whitelist_externals = pandoc
 passenv = HOME
@@ -65,7 +68,7 @@ commands = sphinx-build -d "{toxworkdir}/docs_doctree" doc "{toxworkdir}/docs_ou
 
 [testenv:package_description]
 description = check that the long description is valid
-basepython = python3.7
+basepython = python3.8
 deps = twine >= 1.12.1
        # TODO installing readme-renderer[md] should not be necessary
        readme-renderer[md] >= 24.0
@@ -78,23 +81,22 @@ commands = pip wheel -w {envtmpdir}/build --no-deps .
 
 [testenv:fix_lint]
 description = format the code base to adhere to our styles, and complain about what we cannot do automatically
-basepython = python3.7
+basepython = python3.8
 passenv = {[testenv]passenv}
-          # without PROGRAMDATA cloning using git for Windows will fail with an
-          # `error setting certificate verify locations` error
+          # without PROGRAMDATA cloning using git for Windows will fail with an `error setting certificate verify locations` error
           PROGRAMDATA
           PRE_COMMIT_HOME
 extras = lint
 deps = pre-commit>=2
 skip_install = True
-commands = pre-commit run --all-files --show-diff-on-failure
+commands = pre-commit run --all-files --show-diff-on-failure {posargs}
            python -c 'import pathlib; print("hint: run \{\} install to add checks as pre-commit hook".format(pathlib.Path(r"{envdir}") / "bin" / "pre-commit"))'
 
 [testenv:coverage]
 description = [run locally after tests]: combine coverage data and create report;
               generates a diff coverage against origin/latest (can be changed by setting DIFF_AGAINST env var)
 deps = {[testenv]deps}
-       coverage >= 5.0.1, < 6
+       coverage >= 5.0.1
        diff_cover
 skip_install = True
 passenv = {[testenv]passenv}
@@ -105,7 +107,7 @@ commands = coverage combine
            coverage xml -o {toxworkdir}/coverage.xml
            coverage html -d {toxworkdir}/htmlcov
            diff-cover --compare-branch {env:DIFF_AGAINST:origin/latest} {toxworkdir}/coverage.xml
-depends = py38, py37, pypy3
+depends = py39, py38, py37, pypy3
 parallel_show_output = True
 
 [testenv:codecov]
@@ -149,6 +151,7 @@ source = sourmash/
 python =
   3.7: py37, docs, package_description, coverage, codecov
   3.8: py38, coverage, codecov
+  3.9: py39, coverage, codecov
 
 [flake8]
 max-complexity = 22