diff --git a/MANIFEST b/MANIFEST
index e77ce8f..9584ea4 100644
--- a/MANIFEST
+++ b/MANIFEST
@@ -66,6 +66,7 @@ t/Net-ACME2-get_orders.t
 t/Net-ACME2-HTTP.t
 t/Net-ACME2-JWTMaker.t
 t/Net-ACME2-key-change.t
+t/Net-ACME2-link-alternates.t
 t/Net-ACME2-order-lifecycle.t
 t/Net-ACME2-PromiseUtil.t
 t/Net-ACME2-RetryAfter.t
diff --git a/lib/Net/ACME2.pm b/lib/Net/ACME2.pm
index 3073cda..c54fb86 100644
--- a/lib/Net/ACME2.pm
+++ b/lib/Net/ACME2.pm
@@ -923,9 +923,8 @@ sub _parse_link_alternates {
 
     my @alt_urls;
     for my $link (@links) {
-        if ($link =~ m{<([^>]+)>\s*;\s*rel="alternate"}) {
-            push @alt_urls, $1;
-        }
+        next unless $link =~ m{;\s*rel="alternate"}i;
+        push @alt_urls, $1 if $link =~ m{<([^>]+)>};
     }
 
     return @alt_urls;
diff --git a/t/Net-ACME2-link-alternates.t b/t/Net-ACME2-link-alternates.t
new file mode 100644
index 0000000..d57c0aa
--- /dev/null
+++ b/t/Net-ACME2-link-alternates.t
@@ -0,0 +1,184 @@
+#!/usr/bin/env perl
+
+use strict;
+use warnings;
+
+use Test::More;
+use Test::FailWarnings;
+
+# _parse_link_alternates is a private function in Net::ACME2.
+# We test it directly to verify RFC 8288 compliance:
+# - relation types are case-insensitive (section 2.1.1)
+# - link parameters may appear in any order (section 3)
+
+use Net::ACME2 ();
+
+{
+    package MockResponse;
+
+    sub new {
+        my ($class, %opts) = @_;
+        return bless \%opts, $class;
+    }
+
+    sub header {
+        my ($self, $name) = @_;
+        return $self->{ lc $name };
+    }
+}
+
+# --- No Link header ---
+{
+    my $resp = MockResponse->new();
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is( scalar @urls, 0, 'no Link header returns empty list' );
+}
+
+# --- Single alternate link ---
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>;rel="alternate"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'single alternate link',
+    );
+}
+
+# --- Multiple alternate links (arrayref) ---
+{
+    my $resp = MockResponse->new(
+        link => [
+            '<https://ca.example/cert/alt1>;rel="alternate"',
+            '<https://ca.example/cert/alt2>;rel="alternate"',
+        ],
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1', 'https://ca.example/cert/alt2'],
+        'multiple alternate links as arrayref',
+    );
+}
+
+# --- Non-alternate link is ignored ---
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/directory>;rel="index"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is( scalar @urls, 0, 'non-alternate link ignored' );
+}
+
+# --- Mixed alternate and non-alternate ---
+{
+    my $resp = MockResponse->new(
+        link => [
+            '<https://ca.example/directory>;rel="index"',
+            '<https://ca.example/cert/alt1>;rel="alternate"',
+        ],
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'mixed link types: only alternate extracted',
+    );
+}
+
+# --- RFC 8288 section 2.1.1: relation types are case-insensitive ---
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>;rel="Alternate"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'mixed-case "Alternate" matches (RFC 8288 case-insensitive)',
+    );
+}
+
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>;rel="ALTERNATE"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'uppercase "ALTERNATE" matches (RFC 8288 case-insensitive)',
+    );
+}
+
+# --- Whitespace variations ---
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1> ; rel="alternate"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'extra whitespace around semicolon',
+    );
+}
+
+# --- RFC 8288 section 3: parameters may appear in any order ---
+# The rel parameter does not need to be the first parameter after the URI.
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>; title="cross-signed"; rel="alternate"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'rel after other params (title before rel)',
+    );
+}
+
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>; type="application/pem-certificate-chain"; rel="alternate"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'rel after type param',
+    );
+}
+
+{
+    my $resp = MockResponse->new(
+        link => '<https://ca.example/cert/alt1>; rel="alternate"; title="ISRG Root X2"',
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1'],
+        'rel before other params (rel then title)',
+    );
+}
+
+# --- rel in any position with mixed links ---
+{
+    my $resp = MockResponse->new(
+        link => [
+            '<https://ca.example/directory>; rel="index"',
+            '<https://ca.example/cert/alt1>; title="cross-signed"; rel="alternate"',
+            '<https://ca.example/cert/alt2>; rel="alternate"; title="ISRG Root X2"',
+        ],
+    );
+    my @urls = Net::ACME2::_parse_link_alternates($resp);
+    is_deeply(
+        \@urls,
+        ['https://ca.example/cert/alt1', 'https://ca.example/cert/alt2'],
+        'mixed links with rel in various positions',
+    );
+}
+
+done_testing();