diff --git a/internal/updater/updater.go b/internal/updater/updater.go
index 010e374..6bff815 100644
--- a/internal/updater/updater.go
+++ b/internal/updater/updater.go
@@ -122,8 +122,19 @@ func fetchBounded(url string, limit int64) ([]byte, error) {
 	return body, nil
 }
 
+// trimVersionPrefix removes the "v" the toolchain records with, so a
+// recorded version ("v1.2.3", or a pseudo-version "v0.0.0-…") compares
+// against release tags, which CheckLatest already reports without it.
+func trimVersionPrefix(v string) string {
+	return strings.TrimPrefix(v, "v")
+}
+
 // CompareVersions compares two dotted versions numerically per part.
+// Either side may carry the leading "v" of a recorded version or of a
+// tag; the shapes compare equal, which is what keeps an installation
+// running v1.0.0 from being offered an update to 1.0.0.
 func CompareVersions(a, b string) int {
+	a, b = trimVersionPrefix(a), trimVersionPrefix(b)
 	as, bs := strings.Split(a, "."), strings.Split(b, ".")
 	for i := 0; i < len(as) || i < len(bs); i++ {
 		av, bv := part(as, i), part(bs, i)
diff --git a/internal/updater/updater_test.go b/internal/updater/updater_test.go
index 40a8890..732914a 100644
--- a/internal/updater/updater_test.go
+++ b/internal/updater/updater_test.go
@@ -30,6 +30,13 @@ func TestCompareVersions(t *testing.T) {
 		{"0.6", "0.6.0", 0},
 		{"0.10.0", "0.9.0", 1},
 		{"1.2.3-rc1", "1.2.3", 0}, // suffix ignored per part
+		{"v1.0.0", "1.0.0", 0},    // the recorded version carries the v a tag does
+		{"1.0.0", "v1.0.0", 0},
+		{"v1.1.0", "v1.0.0", 1},
+		{"1.28.0", "1.9.0", 1}, // parts compare numerically, not by character
+		{"1.9.0", "1.28.0", -1},
+		{"1.28.0", "1.128.0", -1},
+		{"v1.28.0", "1.28.0", 0},
 	}
 	for _, tc := range cases {
 		if got := CompareVersions(tc.a, tc.b); got != tc.want {
@@ -60,6 +67,39 @@ func TestCheckLatestParsesTag(t *testing.T) {
 	if got := UpdateAvailable("2.0.0"); got != "" {
 		t.Fatalf("UpdateAvailable(newer local) = %q", got)
 	}
+	// The recorded version carries the "v" the release tag does: an
+	// installation running v1.2.3 must not be offered 1.2.3.
+	if got := UpdateAvailable("v1.2.3"); got != "" {
+		t.Fatalf("UpdateAvailable(v-prefixed current) = %q", got)
+	}
+	if got := UpdateAvailable("v1.2.2"); got != "1.2.3" {
+		t.Fatalf("UpdateAvailable(v-prefixed older) = %q", got)
+	}
+}
+
+// The production bug: an installation running v1.0.0 was offered an
+// update to 1.0.0, because the recorded version and the tag compared
+// unequal through the prefix. SelfUpdate must refuse in place, and it
+// must not download anything on the way.
+func TestSelfUpdateRefusesTheSameVersionThroughThePrefix(t *testing.T) {
+	var downloads int
+	srv := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		if strings.Contains(r.URL.Path, "/releases/download/") {
+			downloads++
+		}
+		_ = json.NewEncoder(w).Encode(map[string]any{"tag_name": "v9.9.9"})
+	}))
+	defer srv.Close()
+	old := ReleaseBase
+	ReleaseBase = srv.URL
+	defer func() { ReleaseBase = old }()
+
+	if _, err := SelfUpdate("v9.9.9"); err == nil || !strings.Contains(err.Error(), "already running") {
+		t.Fatalf("SelfUpdate(v-prefixed current) = %v, want the latest-release refusal", err)
+	}
+	if downloads != 0 {
+		t.Fatalf("%d download requests fired for a same-version update", downloads)
+	}
 }
 
 func TestCheckLatestErrors(t *testing.T) {