diff --git a/changes/28.0.4.md b/changes/28.0.4.md
index badb419cc..18d6b5f3f 100644
--- a/changes/28.0.4.md
+++ b/changes/28.0.4.md
@@ -1 +1,2 @@
 * Fix leaning marks of turned capital F/L (#2137).
+* Fix overlay bar placement of Z with Hook and Z with Swash Tail (#2141).
diff --git a/packages/font-glyphs/src/letter/latin/z.ptl b/packages/font-glyphs/src/letter/latin/z.ptl
index 9202f83be..666e7098c 100644
--- a/packages/font-glyphs/src/letter/latin/z.ptl
+++ b/packages/font-glyphs/src/letter/latin/z.ptl
@@ -234,6 +234,7 @@ glyph-block Letter-Latin-Z : begin
 
 		create-glyph "ZDTail.\(suffix)" : glyph-proc
 			include : MarkSet.capDesc
+			set-base-anchor 'overlay' Middle (CAP / 2)
 			include : capital MODE-ZDESC
 			if serifs : include : serifs CAP
 			if slash  : include : slash  CAP
@@ -258,6 +259,7 @@ glyph-block Letter-Latin-Z : begin
 
 		create-glyph "ZSwash.\(suffix)" : glyph-proc
 			include : MarkSet.capDesc
+			set-base-anchor 'overlay' Middle (CAP / 2)
 			include : capital MODE-ZSWASH
 			if serifs : include : serifs CAP
 			if slash  : include : slash  CAP
@@ -278,6 +280,7 @@ glyph-block Letter-Latin-Z : begin
 
 		create-glyph "zDTail.\(suffix)" : glyph-proc
 			include : MarkSet.p
+			set-base-anchor 'overlay' Middle (XH / 2)
 			include : small MODE-ZDESC
 			if serifs : include : serifs XH
 			if slash  : include : slash  XH
@@ -302,6 +305,7 @@ glyph-block Letter-Latin-Z : begin
 
 		create-glyph "zSwash.\(suffix)" : glyph-proc
 			include : MarkSet.p
+			set-base-anchor 'overlay' Middle (XH / 2)
 			include : small MODE-ZSWASH
 			if serifs : include : serifs XH
 			if slash  : include : slash  XH