diff --git a/internal/lsp/cache/snapshot.go b/internal/lsp/cache/snapshot.go
index b02faac9124..f409d73e1fc 100644
--- a/internal/lsp/cache/snapshot.go
+++ b/internal/lsp/cache/snapshot.go
@@ -98,6 +98,30 @@ func (s *snapshot) getPackages(uri span.URI, m source.ParseMode) (cphs []source.
 	return cphs
 }
 
+func (s *snapshot) KnownImportPaths() map[string]source.Package {
+	s.mu.Lock()
+	defer s.mu.Unlock()
+
+	results := map[string]source.Package{}
+	for _, cph := range s.packages {
+		cachedPkg, err := cph.cached()
+		if err != nil {
+			continue
+		}
+		for importPath, newPkg := range cachedPkg.imports {
+			if oldPkg, ok := results[string(importPath)]; ok {
+				// Using the same trick as NarrowestPackageHandle, prefer non-variants.
+				if len(newPkg.files) < len(oldPkg.(*pkg).files) {
+					results[string(importPath)] = newPkg
+				}
+			} else {
+				results[string(importPath)] = newPkg
+			}
+		}
+	}
+	return results
+}
+
 func (s *snapshot) getPackage(id packageID, m source.ParseMode) *checkPackageHandle {
 	s.mu.Lock()
 	defer s.mu.Unlock()
diff --git a/internal/lsp/source/completion.go b/internal/lsp/source/completion.go
index 905043d814a..70be745229f 100644
--- a/internal/lsp/source/completion.go
+++ b/internal/lsp/source/completion.go
@@ -587,7 +587,15 @@ func (c *completer) selector(sel *ast.SelectorExpr) error {
 		if err != nil {
 			return err
 		}
+		known := c.snapshot.KnownImportPaths()
 		for _, pkgExport := range pkgExports {
+			// If we've seen this import path, use the fully-typed version.
+			if knownPkg, ok := known[pkgExport.Fix.StmtInfo.ImportPath]; ok {
+				c.packageMembers(knownPkg.GetTypes(), &pkgExport.Fix.StmtInfo)
+				continue
+			}
+
+			// Otherwise, continue with untyped proposals.
 			pkg := types.NewPackage(pkgExport.Fix.StmtInfo.ImportPath, pkgExport.Fix.IdentName)
 			for _, export := range pkgExport.Exports {
 				c.found(types.NewVar(0, pkg, export, nil), 0.07, &pkgExport.Fix.StmtInfo)
diff --git a/internal/lsp/source/view.go b/internal/lsp/source/view.go
index 8935f334b06..747c9232ebe 100644
--- a/internal/lsp/source/view.go
+++ b/internal/lsp/source/view.go
@@ -275,6 +275,10 @@ type Snapshot interface {
 	// CheckPackageHandles returns the CheckPackageHandles for the packages
 	// that this file belongs to.
 	CheckPackageHandles(ctx context.Context, f File) ([]CheckPackageHandle, error)
+
+	// KnownImportPaths returns all the packages loaded in this snapshot,
+	// indexed by their import path.
+	KnownImportPaths() map[string]Package
 }
 
 // File represents a source file of any type.
diff --git a/internal/lsp/testdata/summary.txt.golden b/internal/lsp/testdata/summary.txt.golden
index 1b64a5da4d5..51af997c103 100644
--- a/internal/lsp/testdata/summary.txt.golden
+++ b/internal/lsp/testdata/summary.txt.golden
@@ -1,7 +1,7 @@
 -- summary --
 CompletionsCount = 213
 CompletionSnippetCount = 40
-UnimportedCompletionsCount = 2
+UnimportedCompletionsCount = 3
 DeepCompletionsCount = 5
 FuzzyCompletionsCount = 7
 RankedCompletionsCount = 8
diff --git a/internal/lsp/testdata/unimported/unimported.go.in b/internal/lsp/testdata/unimported/unimported.go.in
index c721b314ea5..3b78f7274a3 100644
--- a/internal/lsp/testdata/unimported/unimported.go.in
+++ b/internal/lsp/testdata/unimported/unimported.go.in
@@ -2,7 +2,9 @@ package unimported
 
 func _() {
 	//@unimported("", bytes, context, cryptoslashrand, time, unsafe, externalpackage)
-	bytes. //@unimported(" /", bytesbuffer)
+	// container/ring is extremely unlikely to be imported by anything, so shouldn't have type information.
+	ring.Ring //@unimported("Ring", ringring)
+	signature.Foo //@unimported("Foo", signaturefoo)
 }
 
 // Create markers for unimported std lib packages. Only for use by this test.
@@ -11,6 +13,8 @@ func _() {
 /* rand */ //@item(cryptoslashrand, "rand", "\"crypto/rand\"", "package")
 /* time */ //@item(time, "time", "\"time\"", "package")
 /* unsafe */ //@item(unsafe, "unsafe", "\"unsafe\"", "package")
-/* pkg */ //@item(externalpackage, "pkg", "\"example.com/extramodule/pkg\"", "package" )
+/* pkg */ //@item(externalpackage, "pkg", "\"example.com/extramodule/pkg\"", "package")
 
-/* bytes.Buffer */ //@item(bytesbuffer, "Buffer", "(from \"bytes\")", "var" )
\ No newline at end of file
+/* ring.Ring */ //@item(ringring, "Ring", "(from \"container/ring\")", "var")
+
+/* signature.Foo */ //@item(signaturefoo, "Foo", "func(a string, b int) (c bool) (from \"golang.org/x/tools/internal/lsp/signature\")", "func")
\ No newline at end of file
diff --git a/internal/lsp/testdata/unimported/unimported_cand_type.go b/internal/lsp/testdata/unimported/unimported_cand_type.go
index 765ab19075e..2690c1a4a29 100644
--- a/internal/lsp/testdata/unimported/unimported_cand_type.go
+++ b/internal/lsp/testdata/unimported/unimported_cand_type.go
@@ -1,6 +1,9 @@
 package unimported
 
-import "golang.org/x/tools/internal/lsp/baz"
+import (
+	"golang.org/x/tools/internal/lsp/baz"
+	"golang.org/x/tools/internal/lsp/signature" // provide type information for unimported completions in the other file
+)
 
 func _() {
 	foo.StructFoo{} //@item(litFooStructFoo, "foo.StructFoo{}", "struct{...}", "struct")