diff --git a/ts/test-both/util/filterAndSortContacts_test.ts b/ts/test-both/util/filterAndSortContacts_test.ts
index 870d773567..dbd7bcb208 100644
--- a/ts/test-both/util/filterAndSortContacts_test.ts
+++ b/ts/test-both/util/filterAndSortContacts_test.ts
@@ -10,32 +10,53 @@ describe('filterAndSortContacts', () => {
   const conversations = [
     getDefaultConversation({
       title: '+16505551234',
-      firstName: undefined,
+      e164: '+16505551234',
+      name: undefined,
       profileName: undefined,
     }),
-    getDefaultConversation({ title: 'Carlos Santana' }),
-    getDefaultConversation({ title: 'Aaron Aardvark' }),
-    getDefaultConversation({ title: 'Belinda Beetle' }),
-    getDefaultConversation({ title: 'Belinda Zephyr' }),
+    getDefaultConversation({
+      name: 'Carlos Santana',
+      title: 'Carlos Santana',
+      e164: '+16505559876',
+    }),
+    getDefaultConversation({
+      name: 'Aaron Aardvark',
+      title: 'Aaron Aardvark',
+    }),
+    getDefaultConversation({
+      name: 'Belinda Beetle',
+      title: 'Belinda Beetle',
+    }),
+    getDefaultConversation({
+      name: 'Belinda Zephyr',
+      title: 'Belinda Zephyr',
+    }),
   ];
 
-  it('without a search term, sorts conversations by title', () => {
+  it('without a search term, sorts conversations by title (but puts no-name contacts at the bottom)', () => {
     const titles = filterAndSortContacts(conversations, '').map(
       contact => contact.title
     );
     assert.deepEqual(titles, [
-      '+16505551234',
       'Aaron Aardvark',
       'Belinda Beetle',
       'Belinda Zephyr',
       'Carlos Santana',
+      '+16505551234',
     ]);
   });
 
-  it('filters conversations a search terms', () => {
+  it('can search for contacts by title', () => {
     const titles = filterAndSortContacts(conversations, 'belind').map(
       contact => contact.title
     );
-    assert.deepEqual(titles, ['Belinda Beetle', 'Belinda Zephyr']);
+    assert.sameMembers(titles, ['Belinda Beetle', 'Belinda Zephyr']);
+  });
+
+  it('can search for contacts by phone number (and puts no-name contacts at the bottom)', () => {
+    const titles = filterAndSortContacts(conversations, '650555').map(
+      contact => contact.title
+    );
+    assert.sameMembers(titles, ['Carlos Santana', '+16505551234']);
   });
 });
diff --git a/ts/util/filterAndSortContacts.ts b/ts/util/filterAndSortContacts.ts
index ddf398b0cb..c47cc3219b 100644
--- a/ts/util/filterAndSortContacts.ts
+++ b/ts/util/filterAndSortContacts.ts
@@ -9,7 +9,20 @@ const FUSE_OPTIONS: FuseOptions<ConversationType> = {
   // A small-but-nonzero threshold lets us match parts of E164s better, and makes the
   //   search a little more forgiving.
   threshold: 0.05,
-  keys: ['title', 'name', 'e164'],
+  keys: [
+    {
+      name: 'title',
+      weight: 1,
+    },
+    {
+      name: 'name',
+      weight: 1,
+    },
+    {
+      name: 'e164',
+      weight: 0.5,
+    },
+  ],
 };
 
 const collator = new Intl.Collator();
@@ -23,5 +36,19 @@ export function filterAndSortContacts(
       searchTerm
     );
   }
-  return contacts.concat().sort((a, b) => collator.compare(a.title, b.title));
+
+  return contacts.concat().sort((a, b) => {
+    const aHasName = hasName(a);
+    const bHasName = hasName(b);
+
+    if (aHasName === bHasName) {
+      return collator.compare(a.title, b.title);
+    }
+
+    return aHasName && !bHasName ? -1 : 1;
+  });
+}
+
+function hasName(contact: Readonly<ConversationType>): boolean {
+  return Boolean(contact.name || contact.profileName);
 }