diff --git a/imports/fix.go b/imports/fix.go
index 198094b25d..6e969d03b3 100644
--- a/imports/fix.go
+++ b/imports/fix.go
@@ -238,9 +238,10 @@ type pass struct {
 	used            map[*importInfo]bool
 
 	// Inputs to fix. These can be augmented between successive fix calls.
-	lastTry       bool                    // indicates that this is the last call and fix should clean up as best it can.
-	candidates    []*importInfo           // candidate imports in priority order.
-	knownPackages map[string]*packageInfo // information about all known packages.
+	lastTry        bool                    // indicates that this is the last call and fix should clean up as best it can.
+	addImportNames bool                    // add names to mismatched imports.
+	candidates     []*importInfo           // candidate imports in priority order.
+	knownPackages  map[string]*packageInfo // information about all known packages.
 }
 
 // loadPackageNames saves the package names for everything referenced by imports.
@@ -334,6 +335,23 @@ func (p *pass) fix() bool {
 			astutil.DeleteNamedImport(p.fset, p.f, imp.name, imp.importPath)
 		}
 	}
+
+	if p.addImportNames {
+		for _, imp := range p.f.Imports {
+			if imp.Name != nil {
+				continue
+			}
+			path := strings.Trim(imp.Path.Value, `""`)
+			pkg, ok := p.knownPackages[path]
+			if !ok {
+				continue
+			}
+			if pkg.name != importPathToNameBasic(path, p.srcDir) {
+				imp.Name = &ast.Ident{Name: pkg.name, NamePos: imp.Pos()}
+			}
+		}
+	}
+
 	for _, imp := range selected {
 		astutil.AddNamedImport(p.fset, p.f, imp.name, imp.importPath)
 	}
@@ -421,6 +439,7 @@ func fixImports(fset *token.FileSet, f *ast.File, filename string) error {
 	// the naive algorithm.
 	p = &pass{fset: fset, f: f, srcDir: srcDir}
 	p.pathToName = importPathToName
+	p.addImportNames = true
 	p.otherFiles = otherFiles
 	if p.load() {
 		return nil
@@ -506,7 +525,7 @@ func addGoPathCandidates(pass *pass, refs map[string]map[string]bool, filename s
 			}
 			// If the package name isn't what you'd expect looking
 			// at the import path, add an explicit name.
-			if path.Base(ipath) != pkgName {
+			if importPathToNameBasic(ipath, pass.srcDir) != pkgName {
 				imp.name = pkgName
 			}
 
diff --git a/imports/fix_test.go b/imports/fix_test.go
index 7d71ecd72f..20bc219f03 100644
--- a/imports/fix_test.go
+++ b/imports/fix_test.go
@@ -1350,9 +1350,15 @@ var (
 `
 
 	testConfig{
-		module: packagestest.Module{
-			Name:  "mypkg.com/outpkg",
-			Files: fm{"toformat.go": input},
+		modules: []packagestest.Module{
+			{
+				Name:  "mypkg.com/outpkg",
+				Files: fm{"toformat.go": input},
+			},
+			{
+				Name:  "github.com/foo/v2",
+				Files: fm{"x.go": "package foo\n func Foo(){}\n"},
+			},
 		},
 	}.processTest(t, "mypkg.com/outpkg", "toformat.go", nil, nil, input)
 }
@@ -1363,18 +1369,24 @@ var (
 // that the package name is "mypkg".
 func TestVendorPackage(t *testing.T) {
 	const input = `package p
+import (
+	"fmt"
+	"mypkg.com/mypkg.v1"
+)
+var _, _ = fmt.Print, mypkg.Foo
+`
+
+	const want = `package p
 
 import (
 	"fmt"
 
-	"mypkg.com/mypkg.v1"
+	mypkg "mypkg.com/mypkg.v1"
 )
 
-var (
-	_ = fmt.Print
-	_ = mypkg.Foo
-)
+var _, _ = fmt.Print, mypkg.Foo
 `
+
 	testConfig{
 		gopathOnly: true,
 		module: packagestest.Module{
@@ -1384,7 +1396,7 @@ var (
 				"toformat.go":                    input,
 			},
 		},
-	}.processTest(t, "mypkg.com/outpkg", "toformat.go", nil, nil, input)
+	}.processTest(t, "mypkg.com/outpkg", "toformat.go", nil, nil, want)
 }
 
 func TestInternal(t *testing.T) {
@@ -1562,16 +1574,14 @@ func (t *goimportTest) process(module, file string, contents []byte, opts *Optio
 }
 
 // Tests that added imports are renamed when the import path's base doesn't
-// match its package name. For example, we want to generate:
-//
-//     import cloudbilling "google.golang.org/api/cloudbilling/v1"
+// match its package name.
 func TestRenameWhenPackageNameMismatch(t *testing.T) {
 	const input = `package main
  const Y = bar.X`
 
 	const want = `package main
 
-import bar "foo.com/foo/bar/v1"
+import bar "foo.com/foo/bar/baz"
 
 const Y = bar.X
 `
@@ -1579,8 +1589,42 @@ const Y = bar.X
 		module: packagestest.Module{
 			Name: "foo.com",
 			Files: fm{
-				"foo/bar/v1/x.go": "package bar \n const X = 1",
-				"test/t.go":       input,
+				"foo/bar/baz/x.go": "package bar \n const X = 1",
+				"test/t.go":        input,
+			},
+		},
+	}.processTest(t, "foo.com", "test/t.go", nil, nil, want)
+}
+
+// Tests that an existing import with badly mismatched path/name has its name
+// correctly added. See #28645 and #29041.
+func TestAddNameToMismatchedImport(t *testing.T) {
+	const input = `package main
+
+import (
+"foo.com/surprise"
+"foo.com/v1"
+)
+
+var _, _ = bar.X, v1.Y`
+
+	const want = `package main
+
+import (
+	bar "foo.com/surprise"
+	v1 "foo.com/v1"
+)
+
+var _, _ = bar.X, v1.Y
+`
+
+	testConfig{
+		module: packagestest.Module{
+			Name: "foo.com",
+			Files: fm{
+				"surprise/x.go": "package bar \n const X = 1",
+				"v1/x.go":       "package v1 \n const Y = 1",
+				"test/t.go":     input,
 			},
 		},
 	}.processTest(t, "foo.com", "test/t.go", nil, nil, want)