diff --git a/go/packages/golist.go b/go/packages/golist.go
index 132d28347e..3a0d4b0123 100644
--- a/go/packages/golist.go
+++ b/go/packages/golist.go
@@ -166,12 +166,8 @@ extractQueries:
 		containsCandidates = append(containsCandidates, modifiedPkgs...)
 		containsCandidates = append(containsCandidates, needPkgs...)
 	}
-
-	if len(needPkgs) > 0 {
-		addNeededOverlayPackages(cfg, golistDriver, response, needPkgs)
-		if err != nil {
-			return nil, err
-		}
+	if err := addNeededOverlayPackages(cfg, golistDriver, response, needPkgs); err != nil {
+		return nil, err
 	}
 	// Check candidate packages for containFiles.
 	if len(containFiles) > 0 {
@@ -191,6 +187,9 @@ extractQueries:
 }
 
 func addNeededOverlayPackages(cfg *Config, driver driver, response *responseDeduper, pkgs []string) error {
+	if len(pkgs) == 0 {
+		return nil
+	}
 	dr, err := driver(cfg, pkgs...)
 	if err != nil {
 		return err
@@ -198,6 +197,11 @@ func addNeededOverlayPackages(cfg *Config, driver driver, response *responseDedu
 	for _, pkg := range dr.Packages {
 		response.addPackage(pkg)
 	}
+	_, needPkgs, err := processGolistOverlay(cfg, response.dr)
+	if err != nil {
+		return err
+	}
+	addNeededOverlayPackages(cfg, driver, response, needPkgs)
 	return nil
 }
 
diff --git a/go/packages/golist_overlay.go b/go/packages/golist_overlay.go
index 71ffcd9d55..ce9206f6b3 100644
--- a/go/packages/golist_overlay.go
+++ b/go/packages/golist_overlay.go
@@ -46,7 +46,9 @@ outer:
 					fileExists = true
 				}
 			}
-			if dirContains {
+			// The overlay could have included an entirely new package.
+			isNewPackage := extractPackage(pkg, path, contents)
+			if dirContains || isNewPackage {
 				if !fileExists {
 					pkg.GoFiles = append(pkg.GoFiles, path) // TODO(matloob): should the file just be added to GoFiles?
 					pkg.CompiledGoFiles = append(pkg.CompiledGoFiles, path)
@@ -102,3 +104,30 @@ func extractImports(filename string, contents []byte) ([]string, error) {
 	}
 	return res, nil
 }
+
+func extractPackage(pkg *Package, filename string, contents []byte) bool {
+	// TODO(rstambler): Check the message of the actual error?
+	// It differs between $GOPATH and module mode.
+	if len(pkg.Errors) != 1 {
+		return false
+	}
+	if pkg.Name != "" || pkg.ExportFile != "" {
+		return false
+	}
+	if len(pkg.GoFiles) > 0 || len(pkg.CompiledGoFiles) > 0 || len(pkg.OtherFiles) > 0 {
+		return false
+	}
+	if len(pkg.Imports) > 0 {
+		return false
+	}
+	f, err := parser.ParseFile(token.NewFileSet(), filename, contents, parser.PackageClauseOnly) // TODO(matloob): reuse fileset?
+	if err != nil {
+		return false
+	}
+	if filepath.Base(pkg.PkgPath) != f.Name.Name {
+		return false
+	}
+	pkg.Name = f.Name.Name
+	pkg.Errors = []Error{}
+	return true
+}
diff --git a/go/packages/packages_test.go b/go/packages/packages_test.go
index 0d10533af5..d9ba0f4747 100644
--- a/go/packages/packages_test.go
+++ b/go/packages/packages_test.go
@@ -921,6 +921,87 @@ func testOverlay(t *testing.T, exporter packagestest.Exporter) {
 	}
 }
 
+func TestNewPackagesInOverlay(t *testing.T) { packagestest.TestAll(t, testNewPackagesInOverlay) }
+func testNewPackagesInOverlay(t *testing.T, exporter packagestest.Exporter) {
+	exported := packagestest.Export(t, exporter, []packagestest.Module{{
+		Name: "golang.org/fake",
+		Files: map[string]interface{}{
+			"a/a.go": `package a; import "golang.org/fake/b"; const A = "a" + b.B`,
+			"b/b.go": `package b; import "golang.org/fake/c"; const B = "b" + c.C`,
+			"c/c.go": `package c; const C = "c"`,
+			"d/d.go": `package d; const D = "d"`,
+		}}})
+	defer exported.Cleanup()
+
+	dir := filepath.Dir(filepath.Dir(exported.File("golang.org/fake", "a/a.go")))
+
+	for i, test := range []struct {
+		overlay map[string][]byte
+		want    string // expected value of e.E
+	}{
+		// Overlay with one file.
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"): []byte(`package e; import "golang.org/fake/a"; const E = "e" + a.A`)},
+			`"eabc"`},
+		// Overlay with multiple files in the same package.
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"):      []byte(`package e; import "golang.org/fake/a"; const E = "e" + a.A + underscore`),
+			filepath.Join(dir, "e", "e_util.go"): []byte(`package e; const underscore = "_"`),
+		},
+			`"eabc_"`},
+		// Overlay with multiple files in different packages.
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"):      []byte(`package e; import "golang.org/fake/f"; const E = "e" + f.F + underscore`),
+			filepath.Join(dir, "e", "e_util.go"): []byte(`package e; const underscore = "_"`),
+			filepath.Join(dir, "f", "f.go"):      []byte(`package f; const F = "f"`),
+		},
+			`"ef_"`},
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"):      []byte(`package e; import "golang.org/fake/f"; const E = "e" + f.F + underscore`),
+			filepath.Join(dir, "e", "e_util.go"): []byte(`package e; const underscore = "_"`),
+			filepath.Join(dir, "f", "f.go"):      []byte(`package f; import "golang.org/fake/g"; const F = "f" + g.G`),
+			filepath.Join(dir, "g", "g.go"):      []byte(`package g; const G = "g"`),
+		},
+			`"efg_"`},
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"):      []byte(`package e; import "golang.org/fake/f"; import "golang.org/fake/h"; const E = "e" + f.F + h.H + underscore`),
+			filepath.Join(dir, "e", "e_util.go"): []byte(`package e; const underscore = "_"`),
+			filepath.Join(dir, "f", "f.go"):      []byte(`package f; import "golang.org/fake/g"; const F = "f" + g.G`),
+			filepath.Join(dir, "g", "g.go"):      []byte(`package g; const G = "g"`),
+			filepath.Join(dir, "h", "h.go"):      []byte(`package h; const H = "h"`),
+		},
+			`"efgh_"`},
+		{map[string][]byte{
+			filepath.Join(dir, "e", "e.go"):      []byte(`package e; import "golang.org/fake/f"; const E = "e" + f.F + underscore`),
+			filepath.Join(dir, "e", "e_util.go"): []byte(`package e; const underscore = "_"`),
+			filepath.Join(dir, "f", "f.go"):      []byte(`package f; import "golang.org/fake/g"; const F = "f" + g.G`),
+			filepath.Join(dir, "g", "g.go"):      []byte(`package g; import "golang.org/fake/h"; const G = "g" + h.H`),
+			filepath.Join(dir, "h", "h.go"):      []byte(`package h; const H = "h"`),
+		},
+			`"efgh_"`},
+	} {
+		exported.Config.Overlay = test.overlay
+		exported.Config.Mode = packages.LoadAllSyntax
+		initial, err := packages.Load(exported.Config, "golang.org/fake/e")
+		if err != nil {
+			t.Error(err)
+			continue
+		}
+
+		// Check value of e.E.
+		e := initial[0]
+		eE := constant(e, "E")
+		if eE == nil {
+			t.Errorf("%d. e.E: got nil", i)
+			continue
+		}
+		got := eE.Val().String()
+		if got != test.want {
+			t.Errorf("%d. e.E: got %s, want %s", i, got, test.want)
+		}
+	}
+}
+
 func TestLoadAllSyntaxImportErrors(t *testing.T) {
 	packagestest.TestAll(t, testLoadAllSyntaxImportErrors)
 }
diff --git a/go/packages/packagestest/expect.go b/go/packages/packagestest/expect.go
index 3a1fa3fbd3..3a5d88e8a4 100644
--- a/go/packages/packagestest/expect.go
+++ b/go/packages/packagestest/expect.go
@@ -141,6 +141,9 @@ func (e *Exported) getNotes() error {
 			dirs = append(dirs, filepath.Dir(filename))
 		}
 	}
+	for filename := range e.Config.Overlay {
+		dirs = append(dirs, filepath.Dir(filename))
+	}
 	pkgs, err := packages.Load(e.Config, dirs...)
 	if err != nil {
 		return fmt.Errorf("unable to load packages for directories %s: %v", dirs, err)
diff --git a/internal/lsp/cache/file.go b/internal/lsp/cache/file.go
index db16db614a..9efcccb71c 100644
--- a/internal/lsp/cache/file.go
+++ b/internal/lsp/cache/file.go
@@ -112,9 +112,15 @@ func (f *File) read(ctx context.Context) {
 			return
 		}
 	}
+	// We might have the content saved in an overlay.
+	if content, ok := f.view.Config.Overlay[f.filename]; ok {
+		f.content = content
+		return
+	}
 	// We don't know the content yet, so read it.
 	content, err := ioutil.ReadFile(f.filename)
 	if err != nil {
+		f.view.Logger().Errorf(ctx, "unable to read file %s: %v", f.filename, err)
 		return
 	}
 	f.content = content
diff --git a/internal/lsp/lsp_test.go b/internal/lsp/lsp_test.go
index d6c419a63c..e83686119a 100644
--- a/internal/lsp/lsp_test.go
+++ b/internal/lsp/lsp_test.go
@@ -18,6 +18,7 @@ import (
 	"strings"
 	"testing"
 
+	"golang.org/x/tools/go/packages"
 	"golang.org/x/tools/go/packages/packagestest"
 	"golang.org/x/tools/internal/lsp/cache"
 	"golang.org/x/tools/internal/lsp/diff"
@@ -37,7 +38,7 @@ func testLSP(t *testing.T, exporter packagestest.Exporter) {
 
 	// We hardcode the expected number of test cases to ensure that all tests
 	// are being executed. If a test is added, this number must be changed.
-	const expectedCompletionsCount = 64
+	const expectedCompletionsCount = 65
 	const expectedDiagnosticsCount = 16
 	const expectedFormatCount = 4
 	const expectedDefinitionsCount = 17
@@ -62,7 +63,10 @@ func testLSP(t *testing.T, exporter packagestest.Exporter) {
 	defer exported.Cleanup()
 
 	// Merge the exported.Config with the view.Config.
+	addUnsavedFiles(t, exported.Config, exported)
+
 	cfg := *exported.Config
+
 	cfg.Fset = token.NewFileSet()
 	cfg.Context = context.Background()
 	cfg.ParseFile = func(fset *token.FileSet, filename string, src []byte) (*ast.File, error) {
@@ -174,6 +178,25 @@ func testLSP(t *testing.T, exporter packagestest.Exporter) {
 	})
 }
 
+func addUnsavedFiles(t *testing.T, cfg *packages.Config, exported *packagestest.Exported) {
+	if cfg.Overlay == nil {
+		cfg.Overlay = make(map[string][]byte)
+	}
+	// For now, we hardcode a file that we know is in the testdata.
+	// TODO(rstambler): Figure out a way to do this better.
+	dir := filepath.Dir(filepath.Dir(exported.File("golang.org/x/tools/internal/lsp", filepath.Join("complit", "complit.go"))))
+	cfg.Overlay[filepath.Join(dir, "nodisk", "nodisk.go")] = []byte(`package nodisk
+
+import (
+	"golang.org/x/tools/internal/lsp/foo"
+)
+
+func _() {
+	foo.Foo() //@complete("F", Foo, IntFoo, StructFoo)
+}
+`)
+}
+
 type diagnostics map[span.URI][]protocol.Diagnostic
 type completionItems map[token.Pos]*protocol.CompletionItem
 type completions map[token.Position][]token.Pos
diff --git a/internal/lsp/testdata/nodisk/empty b/internal/lsp/testdata/nodisk/empty
new file mode 100644
index 0000000000..2cecac2c87
--- /dev/null
+++ b/internal/lsp/testdata/nodisk/empty
@@ -0,0 +1 @@
+an empty file so that the directory exists
\ No newline at end of file
diff --git a/internal/span/utf16.go b/internal/span/utf16.go
index e1f5dd80f5..0d356e2b1d 100644
--- a/internal/span/utf16.go
+++ b/internal/span/utf16.go
@@ -56,6 +56,9 @@ func FromUTF16Column(p Point, chr int, content []byte) (Point, error) {
 	if chr <= 1 {
 		return p, nil
 	}
+	if p.Offset() >= len(content) {
+		return p, fmt.Errorf("offset (%v) greater than length of content (%v)", p.Offset(), len(content))
+	}
 	remains := content[p.Offset():]
 	// scan forward the specified number of characters
 	for count := 1; count < chr; count++ {