diff --git a/ir/naming.go b/ir/naming.go
index 94a9fea..dd1481a 100644
--- a/ir/naming.go
+++ b/ir/naming.go
@@ -94,7 +94,7 @@ func wordBoundary(prev, r rune, runes []rune, i int) bool {
 	switch {
 	case carriesCase(r) && (unicode.IsLower(prev) || unicode.IsDigit(prev)):
 		return true // lower/digit -> Upper: "userID" -> user|ID
-	case isCapital(prev) && isCapital(r) && i+1 < len(runes) && unicode.IsLower(runes[i+1]):
+	case acronymTail(prev, r, runes, i):
 		return true // acronym tail: "HTTPServer" -> HTTP|Server
 	case unicode.IsLetter(prev) && unicode.IsDigit(r), unicode.IsDigit(prev) && unicode.IsLetter(r):
 		return true // letter<->digit: "APIKey2" -> ...Key|2
@@ -103,6 +103,31 @@ func wordBoundary(prev, r rune, runes []rune, i int) bool {
 	}
 }
 
+// acronymTail reports whether runes[i] is the last capital of a run and opens
+// the next word — the S of "HTTPServer" — which is two capitals followed by a
+// lowercase letter.
+//
+// At least one of the two capitals must be one lowercasing changes. That is what
+// keeps the rule from splitting its own output: a boundary between two runes
+// lowercasing leaves alone survives into the result still looking like a
+// boundary, so a second pass splits there again (GitHub #336). The lowercase
+// letter the rule looks for need not have been lowercase in the source — "ℤℤA"
+// has none, and lowercasing the A supplies one — so asking only about the source
+// runes either side is not enough to know the pattern will not reappear.
+//
+// Requiring case of both would be too strong in either direction: it would lose
+// ℤ_server, where only the S carries case, and http_ℤerver, where only the P
+// does. Both are pinned in canonicalCases.
+func acronymTail(prev, r rune, runes []rune, i int) bool {
+	if !isCapital(prev) || !isCapital(r) {
+		return false
+	}
+	if !carriesCase(prev) && !carriesCase(r) {
+		return false // neither is lowercased, so the split would reappear
+	}
+	return i+1 < len(runes) && unicode.IsLower(runes[i+1])
+}
+
 // The two boundary rules above ask different questions about a rune, and the
 // difference is what GitHub #187 turned on.
 //
@@ -118,12 +143,15 @@ func wordBoundary(prev, r rune, runes []rune, i int) bool {
 // isCapital asks whether r *belongs to a run of capitals*, which is a question
 // about the letter's form rather than about a transition — the acronym-tail rule
 // splits at the last capital of a run, and ℤ is one of those whether or not
-// lowercasing would change it. Using carriesCase there instead would lose
-// ℤ_server, and using IsUpper alone would lose the titlecase forms.
+// lowercasing would change it. Using carriesCase alone there would lose
+// ℤ_server, and using IsUpper alone would lose the titlecase forms. Which is why
+// the tail rule asks both: isCapital of each rune, and carriesCase of the pair.
 //
-// Both stay idempotent: after one pass the only capitals left are the ones
-// lowercasing does not change, and the tail rule needs a lowercase letter
-// following, which such a run does not produce on its own.
+// The grammar is a fixed point because no rule can fire on its own output. One
+// pass lowercases every rune that carries case, so the two case rules — which
+// each require one at the boundary — have nothing left to fire on, and the
+// letter/digit rule is case-independent and has already been applied everywhere
+// it applies.
 func carriesCase(r rune) bool { return unicode.ToLower(r) != r }
 
 // isCapital reports whether r is a capital letter form — uppercase or titlecase.
diff --git a/ir/naming_grammar_test.go b/ir/naming_grammar_test.go
index a1b6073..ba79fbf 100644
--- a/ir/naming_grammar_test.go
+++ b/ir/naming_grammar_test.go
@@ -66,6 +66,14 @@ var canonicalCases = []struct {
 	{"a run of capitals ends at one with no lowercase form", "\u2124Server", "\u2124_server"},
 	{"and such a letter can be the tail itself", "HTTP\u2124erver", "http_\u2124erver"},
 	{"a titlecase letter opens a run", "\u01C5Bc", "\u01C6_bc"},
+	// GitHub #336. A tail needs case on one side of the split, because a split
+	// between two runes lowercasing leaves alone is one the next pass makes
+	// again. The lowercase letter the rule looks for is not always in the
+	// source: "\u2124\u2124A" has none, and lowercasing the A supplies one, so the pair
+	// below used to segment differently from the spelling one case apart.
+	{"a run of caseless capitals is no tail", "\u2124\u2124A", "\u2124\u2124a"},
+	{"so the lowercase spelling segments the same way", "\u2124\u2124a", "\u2124\u2124a"},
+	{"a caseless run still ends at a cased capital", "\u2124\u2124Ab", "\u2124\u2124_ab"},
 	{"a name with no word rune has no words", "***", ""},
 	{"the empty name is empty", "", ""},
 }
diff --git a/ir/naming_property_test.go b/ir/naming_property_test.go
index 7d9730b..2ad7a2e 100644
--- a/ir/naming_property_test.go
+++ b/ir/naming_property_test.go
@@ -19,6 +19,11 @@ import (
 //
 //   - ℤ, ϒ: IsUpper reports true and ToLower returns them unchanged — a letter
 //     with no lowercase form.
+//   - ℤℤA: two of those before one that does lowercase. The seed beside it,
+//     ℤℤa, was already here and passed; the input that broke idempotence was
+//     the uppercase spelling one mutation away from it, because lowercasing the
+//     A is what supplied the lowercase letter the tail rule looks for
+//     (GitHub #336).
 //   - Dž: titlecase, which is neither IsUpper nor IsLower.
 //   - ẞ: uppercase whose lowercase ß is a different letter.
 //   - İ: uppercase whose lowercase is two runes, so lowercasing changes length.
@@ -29,7 +34,7 @@ import (
 //     Hebrew are cased by nothing at all.
 //   - the rest: the boundaries the grammar splits on, and names with no words.
 var adversarialRunes = []string{
-	"Aℤ", "aℤ", "COUNTℤ", "ℤℤa", "aℤℤb",
+	"Aℤ", "aℤ", "COUNTℤ", "ℤℤa", "ℤℤA", "aℤℤb",
 	"Aϒ", "xDžy", "aẞb", "İstanbul", "Džungla",
 	"café_v2", "́x", "x́",
 	"ᎠᎡ", "ꭰx", "𐐀𐐨", "Δε", "Жx", "中文", "אב",