diff --git a/parser-typechecker/src/Unison/PrettyPrintEnv.hs b/parser-typechecker/src/Unison/PrettyPrintEnv.hs
index 7863c4e6e..b4e19b8ab 100644
--- a/parser-typechecker/src/Unison/PrettyPrintEnv.hs
+++ b/parser-typechecker/src/Unison/PrettyPrintEnv.hs
@@ -41,9 +41,8 @@ fromNames len names = PrettyPrintEnv terms' types' where
 
 fromSuffixNames :: Int -> Names -> PrettyPrintEnv
 fromSuffixNames len names = PrettyPrintEnv terms' types' where
-  terms' r = pickName . Set.map HQ'.toHQ $ Names.suffixedTermName len r names
-  types' r = pickName . Set.map HQ'.toHQ $ Names.suffixedTypeName len r names
-  pickName ns = safeHead . Name.sortNameds toList . HQ.sortByLength $ toList ns
+  terms' r = safeHead $ Names.suffixedTermName len r names
+  types' r = safeHead $ Names.suffixedTypeName len r names
 
 fromNamesDecl :: Int -> Names -> PrettyPrintEnvDecl
 fromNamesDecl len names =
diff --git a/unison-core/src/Unison/Names3.hs b/unison-core/src/Unison/Names3.hs
index 6d7cc172f..ff0043677 100644
--- a/unison-core/src/Unison/Names3.hs
+++ b/unison-core/src/Unison/Names3.hs
@@ -193,8 +193,8 @@ termName length r Names{..} =
   where hq n = HQ'.take length (HQ'.fromNamedReferent n r)
         isConflicted n = R.manyDom n (Names.terms currentNames)
 
-suffixedTypeName :: Int -> Reference -> Names -> Set (HQ'.HashQualified Name)
-suffixedTermName :: Int -> Referent -> Names -> Set (HQ'.HashQualified Name)
+suffixedTypeName :: Int -> Reference -> Names -> [HQ.HashQualified Name]
+suffixedTermName :: Int -> Referent -> Names -> [HQ.HashQualified Name]
 (suffixedTermName,suffixedTypeName) =
   ( suffixedName termName (Names.terms . currentNames) HQ'.fromNamedReferent
   , suffixedName typeName (Names.types . currentNames) HQ'.fromNamedReference )
@@ -202,17 +202,24 @@ suffixedTermName :: Int -> Referent -> Names -> Set (HQ'.HashQualified Name)
   suffixedName fallback getRel hq' length r ns@(getRel -> rel) =
     if R.memberRan r rel
     then go $ toList (R.lookupRan r rel)
-    else fallback length r ns
+    else sort $ map Name.convert $ Set.toList (fallback length r ns)
     where
+      sort = HQ.sortByLength . Name.sortNameds toList
       isConflicted n = R.manyDom n rel
       hq n = HQ'.take length (hq' n r)
-      go ns = case sortOn (\n -> (Name.countSegments n, Name.toText n)) ns of
+      go ns = case sortOn Name.countSegments ns of
         [] -> mempty
-        fqn : _ -> Set.singleton $
-          let n' = shortestUniqueSuffix fqn r rel
-          in if isConflicted fqn then hq n'
-             else HQ'.fromName n'
+        fqns -> Name.sortNameds toList (map f fqns) where
+          f fqn = Name.convert $
+            let n' = shortestUniqueSuffix fqn r rel
+            in if isConflicted fqn then hq n' else HQ'.fromName n'
 
+-- Tries to shorten `fqn` to the smallest suffix that still refers
+-- uniquely to `r`. Uses an efficient logarithmic lookup in the
+-- provided relation.
+--
+-- NB: Only works if the `Ord` instance for `Name` orders based on
+-- `Name.reverseSegments`.
 shortestUniqueSuffix :: Ord r => Name -> r -> Relation Name r -> Name
 shortestUniqueSuffix fqn r rel =
   maybe fqn (Name.convert . reverse) (find isOk suffixes)