diff --git a/benchmarks/sequence_set-normalize.yml b/benchmarks/sequence_set-normalize.yml
index 7755381b..af7d35ed 100644
--- a/benchmarks/sequence_set-normalize.yml
+++ b/benchmarks/sequence_set-normalize.yml
@@ -42,7 +42,7 @@ prelude: |
     end
   end
 
-  def init_unsorted_sets(...)
+  def make_unsorted_sets(...)
     init_sets(...)
       .each do |seqset|
         entries = shuffle_entries(seqset)
@@ -51,6 +51,10 @@ prelude: |
           seqset.append entry
         end
       end
+  end
+
+  def init_unsorted_sets(...)
+    make_unsorted_sets(...)
       .tap do maybe_profile("seqset-normalize-unsorted") end
   end
 
@@ -68,14 +72,30 @@ prelude: |
       .join(",")
   end
 
-  def init_abnormal_sets(...)
+  def make_abnormal_sets(...)
     init_sets(...)
       .each do |seqset|
         seqset.string = abnormal_form(seqset)
       end
+  end
+
+  def init_abnormal_sets(...)
+    make_abnormal_sets(...)
       .tap do maybe_profile("seqset-normalize-abnormal") end
   end
 
+  def init_frozen_unsorted_sets(...)
+    make_unsorted_sets(...)
+      .map(&:freeze)
+      .tap do maybe_profile("seqset-normalize-frozen-unsorted") end
+  end
+
+  def init_frozen_abnormal_sets(...)
+    make_abnormal_sets(...)
+      .map(&:freeze)
+      .tap do maybe_profile("seqset-normalize-frozen-abnormal") end
+  end
+
   # warmup (esp. for JIT)
   WARMUP_RUNS.times do
     init_sets(count: 20, set_size: 100, max: 120).each do |set|
@@ -96,6 +116,12 @@ benchmark:
   - name: "abnormal"
     prelude: $sets = init_abnormal_sets
     script:  $sets.sample.normalize
+  - name: "frozen unsorted"
+    prelude: $sets = init_frozen_unsorted_sets
+    script:  $sets.sample.normalize
+  - name: "frozen abnormal"
+    prelude: $sets = init_frozen_abnormal_sets
+    script:  $sets.sample.normalize
 
 contexts:
   # n.b: can't use anything newer as the baseline: it's over 500x faster!
diff --git a/lib/net/imap/sequence_set.rb b/lib/net/imap/sequence_set.rb
index 15fa6847..cdabb4b7 100644
--- a/lib/net/imap/sequence_set.rb
+++ b/lib/net/imap/sequence_set.rb
@@ -1708,7 +1708,7 @@ def xor!(other)
       #
       # Related: #normalize!, #normalized_string
       def normalize
-        return self if frozen? && (@string.nil? || @string == normalized_string)
+        return self if frozen? && (@string.nil? || normal_string?(@string))
         remain_frozen dup.normalize!
       end
 
@@ -1908,6 +1908,8 @@ def each_parsed_entry(str)
         str&.split(",", -1) do |entry| yield parse_string_entry(entry) end
       end
 
+      def normal_string?(str) normalized_entries? each_parsed_entry str end
+
       def normalized_entries?(entries)
         max = nil
         entries.each do |first, last|