diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 217a195..a348f3f 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -260,6 +260,36 @@ jobs:
           fi
           grep -q -- "--no-verify" "$RUNNER_TEMP/err"
 
+      # cosign v2 reads the release's Sigstore bundles from 2.4 on, with a flag the script adds.
+      - name: Install cosign v2.4
+        uses: sigstore/cosign-installer@6f9f17788090df1f26f669e9d70d6ae9567deba6 # v4.1.2
+        with:
+          cosign-release: "v2.4.1"
+
+      - name: Install the latest release with the script and cosign v2.4
+        run: |
+          set -eu
+          cosign version | grep -q 'GitVersion: *v2\.4\.1'
+          sh install.sh --dir "$RUNNER_TEMP/bin-v2" --no-man
+          "$RUNNER_TEMP/bin-v2/hodeishield" --version
+
+      # Older cosign versions cannot read them: the script must say which version it needs.
+      - name: Install cosign v2.2
+        uses: sigstore/cosign-installer@6f9f17788090df1f26f669e9d70d6ae9567deba6 # v4.1.2
+        with:
+          cosign-release: "v2.2.4"
+
+      - name: The script names the cosign version it needs
+        run: |
+          set -eu
+          cosign version | grep -q 'GitVersion: *v2\.2\.4'
+          if sh install.sh --dir "$RUNNER_TEMP/bin-old" --no-man 2> "$RUNNER_TEMP/err-old"; then
+            echo "::error::install.sh accepted cosign v2.2.4"
+            exit 1
+          fi
+          grep -q "install cosign v3 (or v2.4 or newer)" "$RUNNER_TEMP/err-old"
+          test ! -e "$RUNNER_TEMP/bin-old/hodeishield"
+
   # The repository freshness monitor must go red: its control builds small repositories with a
   # throwaway key, serves them from localhost and checks that every stale, altered, unsigned or
   # missing case fails and the current one passes.
diff --git a/CHANGELOG.md b/CHANGELOG.md
index dc2746d..03a1581 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,15 @@ commands, `--json` output and exit codes. Each release's notes start with its se
 
 ## [Unreleased]
 
+### Fixed
+
+- `install.sh` now checks the release's signature with cosign v2 (2.4 or newer) as well as v3. With
+  cosign v2 it stopped with "the Sigstore signature does not verify" although the release was
+  genuine: the signatures are Sigstore bundles that cosign v2 reads only with `--new-bundle-format`,
+  which the script now adds. With an older cosign it names the version it needs instead. The README
+  and `docs/verifying-releases.md` now say which cosign versions work, and what to add with v2.
+  ([#141](https://github.com/Hodeitek/hodeishield-cli/issues/141))
+
 ## [0.4.0] - 2026-10-12
 
 ### Added
diff --git a/README.md b/README.md
index 7c9e9ac..4cad1bb 100644
--- a/README.md
+++ b/README.md
@@ -154,8 +154,10 @@ less install.sh
 sh install.sh --version $v
 ```
 
-It needs `cosign` to check the archive's signature and stops if it is missing; `--no-verify` skips
-that check (the checksum still runs). `sh install.sh --help` lists the options (`--dir`, `--no-man`).
+It needs `cosign` v3, or v2.4 or newer, to check the archive's signature, and stops if it is missing
+or older; `--no-verify` skips that check (the checksum still runs). To check `install.sh` itself with
+cosign v2 as above, add `--new-bundle-format` to `cosign verify-blob`. `sh install.sh --help` lists
+the options (`--dir`, `--no-man`).
 
 ### Container image
 
diff --git a/docs/verifying-releases.md b/docs/verifying-releases.md
index 87e25f0..b4a15bd 100644
--- a/docs/verifying-releases.md
+++ b/docs/verifying-releases.md
@@ -50,7 +50,9 @@ what the next two steps are for.
 
 ## 3. Verify the Sigstore signature
 
-Requires [`cosign`](https://github.com/sigstore/cosign) (v2 or newer).
+Requires [`cosign`](https://github.com/sigstore/cosign) v3. With cosign v2 (2.4 or newer), add
+`--new-bundle-format` to each `cosign verify-blob` command below: the signatures are Sigstore bundles
+in the format cosign v3 reads by default. Older cosign versions cannot read them.
 
 ```sh
 cosign verify-blob \
diff --git a/install.sh b/install.sh
index 74fbfba..a0252dc 100755
--- a/install.sh
+++ b/install.sh
@@ -16,7 +16,8 @@
 #   --no-verify      skip the cosign signature check (the SHA256SUMS check always runs). Only for
 #                    machines that cannot run cosign; the checksum alone does not prove who built it.
 #
-# Needs curl, tar and sha256sum or shasum; cosign (https://docs.sigstore.dev) unless --no-verify.
+# Needs curl, tar and sha256sum or shasum; cosign v3, or v2.4 or newer (https://docs.sigstore.dev),
+# unless --no-verify.
 
 set -eu
 
@@ -64,6 +65,17 @@ fi
 if [ "$verify" -eq 1 ] && ! command -v cosign > /dev/null 2>&1; then
   die "cosign is required to check the signature: install it (https://docs.sigstore.dev/cosign/system_config/installation/) and run this again. To install without the signature check, pass --no-verify."
 fi
+# The signatures are Sigstore bundles in the format cosign v3 reads by default. cosign v2 reads them
+# from 2.4 on when asked to (--new-bundle-format), and older versions cannot read them at all.
+bundle_format=
+if [ "$verify" -eq 1 ]; then
+  cosign_version=$(cosign version 2> /dev/null | awk '$1 == "GitVersion:" { print $2; exit }')
+  case $cosign_version in
+    v0.* | v1.* | v2.[0-3] | v2.[0-3].*)
+      die "cosign ${cosign_version} cannot read the release's signatures: install cosign v3 (or v2.4 or newer) and run this again." ;;
+    v2.*) bundle_format=--new-bundle-format ;;
+  esac
+fi
 
 case "$(uname -s)" in
   Linux)
@@ -112,7 +124,7 @@ expected=$(awk -v f="${name}.tar.gz" '$2 == f || $2 == "*" f { print $1 }' "${tm
 printf 'Checksum: OK\n'
 
 if [ "$verify" -eq 1 ]; then
-  cosign verify-blob \
+  cosign verify-blob ${bundle_format:+"$bundle_format"} \
     --bundle "${tmp}/${name}.tar.gz.sigstore.json" \
     --certificate-identity "${WORKFLOW}@refs/tags/v${version}" \
     --certificate-oidc-issuer "$ISSUER" \