diff --git a/.github/workflows/publish_binary.yml b/.github/workflows/publish_binary.yml
index 30f801ce..c3ce5fbb 100644
--- a/.github/workflows/publish_binary.yml
+++ b/.github/workflows/publish_binary.yml
@@ -52,7 +52,7 @@ jobs:
       - name: Update downloads
         run: |
           mkdir -p site/pythons/binaries
-          cp "dist/$entry.tar.gz" "dist/$entry.meta" "dist/$entry" \
+          cp "dist/$entry.tar.xz" "dist/$entry.meta" "dist/$entry" \
             site/pythons/binaries/
           cd site/pythons
           ./update.sh
diff --git a/plugins/pyenv-binary/README.md b/plugins/pyenv-binary/README.md
index 817e9a6f..e88537f4 100644
--- a/plugins/pyenv-binary/README.md
+++ b/plugins/pyenv-binary/README.md
@@ -14,6 +14,9 @@ architecture and a compatible libc) and have the recorded system libraries. It
 is not portable across, say, glibc and musl, or to an older glibc; the platform
 and dependency metadata exist to catch that.
 
+Installing a binary package requires `tar` with xz support (typically provided
+by the `xz` package).
+
 ## Commands
 
 ### `pyenv binary package [-v|--verbose] <version>[:<entry>] --archive-base-url <url>`
@@ -29,7 +32,7 @@ Pass `-v` to show build progress from `pyenv install`.
 ```sh
 pyenv binary package 3.12.7 \
   --archive-base-url https://example.com/binaries
-# On Debian 12 x86_64, writes 3.12.7-debian-12-x86_64.tar.gz,
+# On Debian 12 x86_64, writes 3.12.7-debian-12-x86_64.tar.xz,
 # its .meta file and a `3.12.7-debian-12-x86_64' definition.
 
 pyenv binary package 3.12.7:company-python \
@@ -54,7 +57,7 @@ pyenv binary package-name 3.12.7
 
 ### `pyenv binary save <version> [<output-dir>] [--name <name>]`
 
-Packs an installed version into `<version>-<platform>.tar.gz` (relative paths)
+Packs an installed version into `<version>-<platform>.tar.xz` (relative paths)
 and writes `<version>-<platform>.meta` describing the build platform (OS, arch,
 distro and libc version) and the system libraries the build links against. Use
 `--name` to set a different base name for both files.
@@ -78,7 +81,7 @@ needs are present.
 
 ```sh
 pyenv binary generate-installer ./dist/3.12.7-linux-x86_64.meta \
-  --archive-url https://example.com/3.12.7-linux-x86_64.tar.gz \
+  --archive-url https://example.com/3.12.7-linux-x86_64.tar.xz \
   -o "$(pyenv root)/plugins/python-build/share/python-build/3.12.7-linux-x86_64"
 
 pyenv install 3.12.7-linux-x86_64
diff --git a/plugins/pyenv-binary/libexec/pyenv-binary-package b/plugins/pyenv-binary/libexec/pyenv-binary-package
index f86666e2..77479f2a 100755
--- a/plugins/pyenv-binary/libexec/pyenv-binary-package
+++ b/plugins/pyenv-binary/libexec/pyenv-binary-package
@@ -7,7 +7,7 @@
 #   Installs <version> from source under a separate entry name, saves it as a
 #   binary package, then emits a python-build definition for that package.
 #   The archive, metadata and definition are written to the current directory
-#   as <entry>.tar.gz, <entry>.meta and <entry>.
+#   as <entry>.tar.xz, <entry>.meta and <entry>.
 #
 #   <version>             A version `pyenv install' knows how to build.
 #   <entry>               The optional name to build under and install the
@@ -16,7 +16,7 @@
 #   -v,--verbose          Show build progress from `pyenv install'.
 #   --archive-base-url <url>
 #                         Where the archive will be hosted; the definition
-#                         downloads it from <url>/<entry>.tar.gz.
+#                         downloads it from <url>/<entry>.tar.xz.
 #
 set -e
 [ -n "$PYENV_DEBUG" ] && set -x
@@ -80,4 +80,4 @@ pyenv-install ${verbose:+--verbose} "$spec"
 pyenv-binary-save "$entry" "$PWD" --name "$entry"
 
 pyenv-binary-generate-installer "${entry}.meta" \
-  --archive-url "${archive_base_url%/}/${entry}.tar.gz" -o "$entry"
+  --archive-url "${archive_base_url%/}/${entry}.tar.xz" -o "$entry"
diff --git a/plugins/pyenv-binary/libexec/pyenv-binary-save b/plugins/pyenv-binary/libexec/pyenv-binary-save
index b940123a..444c02cc 100755
--- a/plugins/pyenv-binary/libexec/pyenv-binary-save
+++ b/plugins/pyenv-binary/libexec/pyenv-binary-save
@@ -4,7 +4,7 @@
 #
 # Usage: pyenv binary save <version> [<output-dir>] [--name <name>]
 #
-#   Packs an installed version into a relocatable .tar.gz (relative paths) and
+#   Packs an installed version into a relocatable .tar.xz (relative paths) and
 #   writes a metadata file listing the build platform and the system libraries
 #   it links against, so an installer can check compatibility before unpacking.
 #
@@ -134,10 +134,10 @@ system_deps() {
 
 mkdir -p "$output_dir"
 package_name="${package_name:-${version}-${platform}}"
-archive="${package_name}.tar.gz"
+archive="${package_name}.tar.xz"
 metadata="${package_name}.meta"
 
-tar -C "$(dirname "$prefix")" -czf "${output_dir}/${archive}" "$(basename "$prefix")"
+tar -C "$(dirname "$prefix")" -cJf "${output_dir}/${archive}" "$(basename "$prefix")"
 
 {
   echo "# pyenv-binary metadata"
diff --git a/plugins/pyenv-binary/test/package.bats b/plugins/pyenv-binary/test/package.bats
index 4186a1c8..40e875a9 100644
--- a/plugins/pyenv-binary/test/package.bats
+++ b/plugins/pyenv-binary/test/package.bats
@@ -66,10 +66,10 @@ pyenv-install --list --bare
   run pyenv-binary-package 3.12.7 --archive-base-url http://example.com/binaries
   assert_success
   assert [ -d "${PYENV_ROOT}/versions/3.12.7-debian-12-x86_64" ]
-  assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-debian-12-x86_64.tar.gz" ]
+  assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-debian-12-x86_64.tar.xz" ]
   assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-debian-12-x86_64.meta" ]
   run grep '^ARCHIVE_URL=' "${BATS_TEST_TMPDIR}/3.12.7-debian-12-x86_64"
-  assert_success "ARCHIVE_URL=http://example.com/binaries/3.12.7-debian-12-x86_64.tar.gz"
+  assert_success "ARCHIVE_URL=http://example.com/binaries/3.12.7-debian-12-x86_64.tar.xz"
 }
 
 @test "rejects an entry name containing a slash" {
@@ -102,10 +102,10 @@ generate-installer"
     --archive-base-url http://example.com/binaries
   assert_success
   assert [ -d "${PYENV_ROOT}/versions/3.12.7-test" ]
-  assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-test.tar.gz" ]
+  assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-test.tar.xz" ]
   assert [ -f "${BATS_TEST_TMPDIR}/3.12.7-test.meta" ]
   run grep '^ARCHIVE_URL=' "${BATS_TEST_TMPDIR}/3.12.7-test"
-  assert_success "ARCHIVE_URL=http://example.com/binaries/3.12.7-test.tar.gz"
+  assert_success "ARCHIVE_URL=http://example.com/binaries/3.12.7-test.tar.xz"
 }
 
 @test "correctly joins archive base url with a trailing slash" {
@@ -127,5 +127,5 @@ done
   run pyenv-binary-package 3.12.7:3.12.7-test \
     --archive-base-url http://example.com/binaries/
   assert_success
-  assert_line "pyenv-binary-generate-installer --archive-url http://example.com/binaries/3.12.7-test.tar.gz"
+  assert_line "pyenv-binary-generate-installer --archive-url http://example.com/binaries/3.12.7-test.tar.xz"
 }
diff --git a/plugins/pyenv-binary/test/save.bats b/plugins/pyenv-binary/test/save.bats
index 11afe55e..62e0fe83 100644
--- a/plugins/pyenv-binary/test/save.bats
+++ b/plugins/pyenv-binary/test/save.bats
@@ -33,13 +33,13 @@ platform() {
 @test "packages an installed version" {
   create_version "3.12.7"
   local out="${BATS_TEST_TMPDIR}/dist"
-  local archive="${out}/3.12.7-$(platform).tar.gz"
+  local archive="${out}/3.12.7-$(platform).tar.xz"
 
   run pyenv-binary-save "3.12.7" "$out"
-  assert_success "Saved 3.12.7-$(platform).tar.gz and 3.12.7-$(platform).meta to $out"
+  assert_success "Saved 3.12.7-$(platform).tar.xz and 3.12.7-$(platform).meta to $out"
   assert [ -f "$archive" ]
   assert [ -f "${out}/3.12.7-$(platform).meta" ]
-  run tar -tzf "$archive"
+  run tar -tJf "$archive"
   assert_success
   assert_line 0 "3.12.7/"
 }
@@ -49,10 +49,10 @@ platform() {
   local out="${BATS_TEST_TMPDIR}/dist"
 
   run pyenv-binary-save "3.12.7" "$out" --name "custom"
-  assert_success "Saved custom.tar.gz and custom.meta to $out"
-  assert [ -f "${out}/custom.tar.gz" ]
+  assert_success "Saved custom.tar.xz and custom.meta to $out"
+  assert [ -f "${out}/custom.tar.xz" ]
   run grep '^archive=' "${out}/custom.meta"
-  assert_success "archive=custom.tar.gz"
+  assert_success "archive=custom.tar.xz"
 }
 
 @test "fails when --name has no value" {
@@ -76,7 +76,7 @@ platform() {
   assert_success
   assert_line "version=3.12.7"
   assert_line "platform=$(platform)"
-  assert_line "archive=3.12.7-$(platform).tar.gz"
+  assert_line "archive=3.12.7-$(platform).tar.xz"
 }
 
 @test "records the original installation prefix" {
@@ -94,7 +94,7 @@ platform() {
 
   PATH="$(path_without readelf)" run pyenv-binary-save "3.12.7" "${BATS_TEST_TMPDIR}/dist"
   assert_failure "pyenv-binary: need readelf to inspect shared libraries"
-  assert [ ! -e "${BATS_TEST_TMPDIR}/dist/3.12.7-$(platform).tar.gz" ]
+  assert [ ! -e "${BATS_TEST_TMPDIR}/dist/3.12.7-$(platform).tar.xz" ]
 }
 
 @test "records only direct libraries resolved outside the prefix" {
diff --git a/test/Dockerfile b/test/Dockerfile
index 58fd3f21..732e6438 100644
--- a/test/Dockerfile
+++ b/test/Dockerfile
@@ -12,7 +12,7 @@ FROM bash:$BASH
     apk add sed coreutils findutils \
   ;fi
   # Bats
-  RUN apk add --update parallel ncurses git binutils \
+  RUN apk add --update parallel ncurses git binutils xz \
         && mkdir -p ~/.parallel \
         && touch ~/.parallel/will-cite
   COPY --from=bats /root/bats-core /root/bats-core