diff --git a/CHANGES.rst b/CHANGES.rst
index 1f178f5c200..b3e69ef489c 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -112,6 +112,10 @@ Bugs fixed
 * #12425: Use Docutils' SVG processing in the HTML builder
   and remove Sphinx's custom logic.
   Patch by Tunç Başar Köse.
+* #12391: Adjust scoring of matches during HTML search so that document main
+  titles tend to rank higher than subsection titles. In addition, boost matches
+  on the name of programming domain objects relative to title/subtitle matches.
+  Patch by James Addison and Will Lachance.
 
 Testing
 -------
diff --git a/sphinx/themes/basic/static/searchtools.js b/sphinx/themes/basic/static/searchtools.js
index eaed90953f4..b08d58c9b9b 100644
--- a/sphinx/themes/basic/static/searchtools.js
+++ b/sphinx/themes/basic/static/searchtools.js
@@ -328,13 +328,14 @@ const Search = {
     for (const [title, foundTitles] of Object.entries(allTitles)) {
       if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) {
         for (const [file, id] of foundTitles) {
-          let score = Math.round(100 * queryLower.length / title.length)
+          const score = Math.round(Scorer.title * queryLower.length / title.length);
+          const boost = titles[file] === title ? 1 : 0;  // add a boost for document titles
           normalResults.push([
             docNames[file],
             titles[file] !== title ? `${titles[file]} > ${title}` : title,
             id !== null ? "#" + id : "",
             null,
-            score,
+            score + boost,
             filenames[file],
           ]);
         }
diff --git a/tests/js/fixtures/titles/searchindex.js b/tests/js/fixtures/titles/searchindex.js
new file mode 100644
index 00000000000..56855ca9a1b
--- /dev/null
+++ b/tests/js/fixtures/titles/searchindex.js
@@ -0,0 +1 @@
+Search.setIndex({"alltitles": {"Main Page": [[0, null]], "Relevance": [[0, "relevance"], [1, null]]}, "docnames": ["index", "relevance"], "envversion": {"sphinx": 61, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2}, "filenames": ["index.rst", "relevance.rst"], "indexentries": {"example (class in relevance)": [[0, "relevance.Example", false]], "module": [[0, "module-relevance", false]], "relevance": [[0, "module-relevance", false]], "relevance (relevance.example attribute)": [[0, "relevance.Example.relevance", false]]}, "objects": {"": [[0, 0, 0, "-", "relevance"]], "relevance": [[0, 1, 1, "", "Example"]], "relevance.Example": [[0, 2, 1, "", "relevance"]]}, "objnames": {"0": ["py", "module", "Python module"], "1": ["py", "class", "Python class"], "2": ["py", "attribute", "Python attribute"]}, "objtypes": {"0": "py:module", "1": "py:class", "2": "py:attribute"}, "terms": {"": [0, 1], "A": 1, "For": 1, "In": [0, 1], "against": 0, "also": 1, "an": 0, "answer": 0, "appear": 1, "ar": 1, "area": 0, "ask": 0, "attribut": 0, "built": 1, "can": [0, 1], "class": 0, "code": [0, 1], "consid": 1, "contain": 0, "context": 0, "corpu": 1, "could": 1, "demonstr": 0, "describ": 1, "detail": 1, "determin": 1, "docstr": 0, "document": [0, 1], "domain": 1, "engin": 0, "exampl": [0, 1], "extract": 0, "find": 0, "found": 0, "from": 0, "function": 1, "ha": 1, "handl": 0, "happen": 1, "head": 0, "help": 0, "highli": 1, "how": 0, "i": [0, 1], "improv": 0, "inform": 0, "intend": 0, "issu": 1, "itself": 1, "knowledg": 0, "languag": 1, "less": 1, "like": [0, 1], "match": 0, "mention": 1, "name": [0, 1], "object": 0, "one": 1, "onli": 1, "other": 0, "page": 1, "part": 1, "particular": 0, "printf": 1, "program": 1, "project": 0, "queri": [0, 1], "question": 0, "re": 0, "rel": 0, "research": 0, "result": 1, "sai": 0, "same": 1, "score": 0, "search": [0, 1], "seem": 0, "softwar": 1, "some": 1, "sphinx": 0, "straightforward": 1, "subject": 0, "subsect": 0, "term": [0, 1], "test": 0, "text": 0, "than": 1, "thei": 0, "them": 0, "thi": 0, "titl": 0, "user": [0, 1], "we": [0, 1], "when": 0, "whether": 1, "within": 0, "would": 1}, "titles": ["Main Page", "Relevance"], "titleterms": {"main": 0, "page": 0, "relev": [0, 1]}})
\ No newline at end of file
diff --git a/tests/js/roots/titles/conf.py b/tests/js/roots/titles/conf.py
new file mode 100644
index 00000000000..e5f6bb97a20
--- /dev/null
+++ b/tests/js/roots/titles/conf.py
@@ -0,0 +1,6 @@
+import os
+import sys
+
+sys.path.insert(0, os.path.abspath('.'))
+
+extensions = ['sphinx.ext.autodoc']
diff --git a/tests/js/roots/titles/index.rst b/tests/js/roots/titles/index.rst
new file mode 100644
index 00000000000..464cd954b5c
--- /dev/null
+++ b/tests/js/roots/titles/index.rst
@@ -0,0 +1,20 @@
+Main Page
+=========
+
+This is the main page of the ``titles`` test project.
+
+In particular, this test project is intended to demonstrate how Sphinx
+can handle scoring of query matches against document titles and subsection
+heading titles relative to other document matches such as terms found within
+document text and object names extracted from code.
+
+Relevance
+---------
+
+In the context of search engines, we can say that a document is **relevant**
+to a user's query when it contains information that seems likely to help them
+find an answer to a question they're asking, or to improve their knowledge of
+the subject area they're researching.
+
+.. automodule:: relevance
+   :members:
diff --git a/tests/js/roots/titles/relevance.py b/tests/js/roots/titles/relevance.py
new file mode 100644
index 00000000000..c4d0eec557f
--- /dev/null
+++ b/tests/js/roots/titles/relevance.py
@@ -0,0 +1,7 @@
+class Example:
+    """Example class"""
+    num_attribute = 5
+    text_attribute = "string"
+
+    relevance = "testing"
+    """attribute docstring"""
diff --git a/tests/js/roots/titles/relevance.rst b/tests/js/roots/titles/relevance.rst
new file mode 100644
index 00000000000..18f494fe109
--- /dev/null
+++ b/tests/js/roots/titles/relevance.rst
@@ -0,0 +1,13 @@
+Relevance
+=========
+
+In some domains, it can be straightforward to determine whether a search result
+is relevant to the user's query.
+
+For example, if we are in a software programming language domain, and a user
+has issued a query for the term ``printf``, then we could consider a document
+in the corpus that describes a built-in language function with the same name
+as (highly) relevant.  A document that only happens to mention the ``printf``
+function name as part of some example code that appears on the page would
+also be relevant, but likely less relevant than the one that describes the
+function itself in detail.
diff --git a/tests/js/searchtools.js b/tests/js/searchtools.js
index d020e40d904..a71047dae9f 100644
--- a/tests/js/searchtools.js
+++ b/tests/js/searchtools.js
@@ -7,6 +7,23 @@ describe('Basic html theme search', function() {
       return req.responseText;
   }
 
+  function checkRanking(expectedRanking, results) {
+    let [nextExpected, ...remainingItems] = expectedRanking;
+
+    for (result of results.reverse()) {
+      if (!nextExpected) break;
+
+      let [expectedPage, expectedTitle, expectedTarget] = nextExpected;
+      let [page, title, target] = result;
+
+      if (page == expectedPage && title == expectedTitle && target == expectedTarget) {
+        [nextExpected, ...remainingItems] = remainingItems;
+      }
+    }
+
+    expect(remainingItems.length).toEqual(0);
+  }
+
   describe('terms search', function() {
 
     it('should find "C++" when in index', function() {
@@ -76,7 +93,7 @@ describe('Basic html theme search', function() {
           'Main Page',
           '',
           null,
-          100,
+          16,
           'index.rst'
         ]
       ];
@@ -85,6 +102,66 @@ describe('Basic html theme search', function() {
 
   });
 
+  describe('search result ranking', function() {
+
+    /*
+     * These tests should not proscribe precise expected ordering of search
+     * results; instead each test case should describe a single relevance rule
+     * that helps users to locate relevant information efficiently.
+     *
+     * If you think that one of the rules seems to be poorly-defined or is
+     * limiting the potential for search algorithm improvements, please check
+     * for existing discussion/bugreports related to it on GitHub[1] before
+     * creating one yourself. Suggestions for possible improvements are also
+     * welcome.
+     *
+     * [1] - https://github.com/sphinx-doc/sphinx.git/
+     */
+
+    it('should score a code module match above a page-title match', function() {
+      eval(loadFixture("titles/searchindex.js"));
+
+      expectedRanking = [
+        ['index', 'relevance', '#module-relevance'],  /* py:module documentation */
+        ['relevance', 'Relevance', ''],  /* main title */
+      ];
+
+      searchParameters = Search._parseQuery('relevance');
+      results = Search._performSearch(...searchParameters);
+
+      checkRanking(expectedRanking, results);
+    });
+
+    it('should score a main-title match above an object member match', function() {
+      eval(loadFixture("titles/searchindex.js"));
+
+      expectedRanking = [
+        ['relevance', 'Relevance', ''],  /* main title */
+        ['index', 'relevance.Example.relevance', '#module-relevance'],  /* py:class attribute */
+      ];
+
+      searchParameters = Search._parseQuery('relevance');
+      results = Search._performSearch(...searchParameters);
+
+      checkRanking(expectedRanking, results);
+    });
+
+    it('should score a main-title match above a subheading-title match', function() {
+      eval(loadFixture("titles/searchindex.js"));
+
+      expectedRanking = [
+        ['relevance', 'Relevance', ''],  /* main title */
+        ['index', 'Main Page > Relevance', '#relevance'],  /* subsection heading title */
+      ];
+
+      searchParameters = Search._parseQuery('relevance');
+      results = Search._performSearch(...searchParameters);
+
+      checkRanking(expectedRanking, results);
+    });
+
+  });
+
 });
 
 describe("htmlToText", function() {