diff --git a/util/stringsx/stringsx.go b/util/stringsx/stringsx.go
new file mode 100644
index 000000000..6c7a8d20d
--- /dev/null
+++ b/util/stringsx/stringsx.go
@@ -0,0 +1,52 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+// Package stringsx provides additional string manipulation functions
+// that aren't in the standard library's strings package or go4.org/mem.
+package stringsx
+
+import (
+	"unicode"
+	"unicode/utf8"
+)
+
+// CompareFold returns -1, 0, or 1 depending on whether a < b, a == b, or a > b,
+// like cmp.Compare, but case insensitively.
+func CompareFold(a, b string) int {
+	// Track our position in both strings
+	ia, ib := 0, 0
+	for ia < len(a) && ib < len(b) {
+		ra, wa := nextRuneLower(a[ia:])
+		rb, wb := nextRuneLower(b[ib:])
+		if ra < rb {
+			return -1
+		}
+		if ra > rb {
+			return 1
+		}
+		ia += wa
+		ib += wb
+		if wa == 0 || wb == 0 {
+			break
+		}
+	}
+
+	// If we've reached here, one or both strings are exhausted
+	// The shorter string is "less than" if they match up to this point
+	switch {
+	case ia == len(a) && ib == len(b):
+		return 0
+	case ia == len(a):
+		return -1
+	default:
+		return 1
+	}
+}
+
+// nextRuneLower returns the next rune in the string, lowercased, along with its
+// original (consumed) width in bytes. If the string is empty, it returns
+// (utf8.RuneError, 0)
+func nextRuneLower(s string) (r rune, width int) {
+	r, width = utf8.DecodeRuneInString(s)
+	return unicode.ToLower(r), width
+}
diff --git a/util/stringsx/stringsx_test.go b/util/stringsx/stringsx_test.go
new file mode 100644
index 000000000..8575c0b27
--- /dev/null
+++ b/util/stringsx/stringsx_test.go
@@ -0,0 +1,78 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package stringsx
+
+import (
+	"cmp"
+	"strings"
+	"testing"
+)
+
+func TestCompareFold(t *testing.T) {
+	tests := []struct {
+		a, b string
+	}{
+		// Basic ASCII cases
+		{"", ""},
+		{"a", "a"},
+		{"a", "A"},
+		{"A", "a"},
+		{"a", "b"},
+		{"b", "a"},
+		{"abc", "ABC"},
+		{"ABC", "abc"},
+		{"abc", "abd"},
+		{"abd", "abc"},
+
+		// Length differences
+		{"abc", "ab"},
+		{"ab", "abc"},
+
+		// Unicode cases
+		{"世界", "世界"},
+		{"Hello世界", "hello世界"},
+		{"世界Hello", "世界hello"},
+		{"世界", "世界x"},
+		{"世界x", "世界"},
+
+		// Special case folding examples
+		{"ß", "ss"},      // German sharp s
+		{"fi", "fi"},      // fi ligature
+		{"Σ", "σ"},       // Greek sigma
+		{"İ", "i\u0307"}, // Turkish dotted I
+
+		// Mixed cases
+		{"HelloWorld", "helloworld"},
+		{"HELLOWORLD", "helloworld"},
+		{"helloworld", "HELLOWORLD"},
+		{"HelloWorld", "helloworld"},
+		{"helloworld", "HelloWorld"},
+
+		// Edge cases
+		{" ", " "},
+		{"1", "1"},
+		{"123", "123"},
+		{"!@#", "!@#"},
+	}
+
+	wants := []int{}
+	for _, tt := range tests {
+		got := CompareFold(tt.a, tt.b)
+		want := cmp.Compare(strings.ToLower(tt.a), strings.ToLower(tt.b))
+		if got != want {
+			t.Errorf("CompareFold(%q, %q) = %v, want %v", tt.a, tt.b, got, want)
+		}
+		wants = append(wants, want)
+	}
+
+	if n := testing.AllocsPerRun(1000, func() {
+		for i, tt := range tests {
+			if CompareFold(tt.a, tt.b) != wants[i] {
+				panic("unexpected")
+			}
+		}
+	}); n > 0 {
+		t.Errorf("allocs = %v; want 0", int(n))
+	}
+}