diff --git a/internal/lsp/fake/editor.go b/internal/lsp/fake/editor.go
index 14ab7ef3eb..79be3a8712 100644
--- a/internal/lsp/fake/editor.go
+++ b/internal/lsp/fake/editor.go
@@ -288,7 +288,10 @@ func (e *Editor) SaveBuffer(ctx context.Context, path string) error {
 	if err := e.FormatBuffer(ctx, path); err != nil {
 		return fmt.Errorf("formatting before save: %w", err)
 	}
+	return e.SaveBufferWithoutActions(ctx, path)
+}
 
+func (e *Editor) SaveBufferWithoutActions(ctx context.Context, path string) error {
 	e.mu.Lock()
 	buf, ok := e.buffers[path]
 	if !ok {
diff --git a/internal/lsp/regtest/diagnostics_114_test.go b/internal/lsp/regtest/diagnostics_114_test.go
index 39f5667d53..5a8540951b 100644
--- a/internal/lsp/regtest/diagnostics_114_test.go
+++ b/internal/lsp/regtest/diagnostics_114_test.go
@@ -2,13 +2,14 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// +build 1.14
+//+build go1.14
 
 package regtest
 
 import (
 	"testing"
 
+	"golang.org/x/tools/internal/lsp"
 	"golang.org/x/tools/internal/lsp/fake"
 	"golang.org/x/tools/internal/lsp/protocol"
 )
@@ -122,3 +123,40 @@ func main() {
 		)
 	}, WithProxy(ardanLabsProxy))
 }
+
+func TestNewFileBadImports_Issue36960(t *testing.T) {
+	const simplePackage = `
+-- go.mod --
+module mod.com
+
+go 1.14
+-- a/a1.go --
+package a
+
+import "fmt"
+
+func _() {
+	fmt.Println("hi")
+}
+`
+	runner.Run(t, simplePackage, func(t *testing.T, env *Env) {
+		env.OpenFile("a/a1.go")
+		env.CreateBuffer("a/a2.go", ``)
+		if err := env.Editor.SaveBufferWithoutActions(env.Ctx, "a/a2.go"); err != nil {
+			t.Fatal(err)
+		}
+		env.Await(
+			OnceMet(
+				CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidSave), 1),
+				NoDiagnostics("a/a1.go"),
+			),
+		)
+		env.EditBuffer("a/a2.go", fake.NewEdit(0, 0, 0, 0, `package a`))
+		env.Await(
+			OnceMet(
+				CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidChange), 1),
+				NoDiagnostics("a/a1.go"),
+			),
+		)
+	})
+}
diff --git a/internal/lsp/regtest/diagnostics_test.go b/internal/lsp/regtest/diagnostics_test.go
index 6a5f016e51..6c77725bdf 100644
--- a/internal/lsp/regtest/diagnostics_test.go
+++ b/internal/lsp/regtest/diagnostics_test.go
@@ -293,8 +293,10 @@ func main() {}
 			// package renaming was fully processed. Therefore, in order for this
 			// test to actually exercise the bug, we must wait until that work has
 			// completed.
-			NoDiagnostics("a.go"),
-			CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidChange), 1),
+			OnceMet(
+				CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidChange), 1),
+				NoDiagnostics("a.go"),
+			),
 		)
 	})
 }
@@ -473,7 +475,13 @@ func f() {
 `
 	runner.Run(t, noModule, func(t *testing.T, env *Env) {
 		env.OpenFile("a.go")
-		env.Await(NoDiagnostics("a.go"), EmptyShowMessage(""))
+		env.Await(
+			OnceMet(
+				CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidOpen), 1),
+				NoDiagnostics("a.go"),
+			),
+			EmptyShowMessage(""),
+		)
 		// introduce an error, expect no Show Message
 		env.RegexpReplace("a.go", "func", "fun")
 		env.Await(env.DiagnosticAtRegexp("a.go", "fun"), EmptyShowMessage(""))
@@ -514,7 +522,10 @@ func main() {
 		}
 		badFile := fmt.Sprintf("%s/found packages main (main.go) and x (x.go) in %s/src/x", dir, env.Sandbox.GOPATH())
 		env.Await(
-			EmptyDiagnostics("x/main.go"),
+			OnceMet(
+				CompletedWork(lsp.DiagnosticWorkTitle(lsp.FromDidChange), 1),
+				EmptyDiagnostics("x/main.go"),
+			),
 			NoDiagnostics(badFile),
 		)
 	}, InGOPATH())
diff --git a/internal/lsp/regtest/env.go b/internal/lsp/regtest/env.go
index 08fc842100..b81a1aa729 100644
--- a/internal/lsp/regtest/env.go
+++ b/internal/lsp/regtest/env.go
@@ -479,7 +479,9 @@ func EmptyDiagnostics(name string) Expectation {
 }
 
 // NoDiagnostics asserts that no diagnostics are sent for the
-// workspace-relative path name.
+// workspace-relative path name. It should be used primarily in conjunction
+// with a OnceMet, as it has to check that all outstanding diagnostics have
+// already been delivered.
 func NoDiagnostics(name string) Expectation {
 	check := func(s State) (Verdict, interface{}) {
 		if _, ok := s.diagnostics[name]; !ok {
@@ -489,7 +491,7 @@ func NoDiagnostics(name string) Expectation {
 	}
 	return SimpleExpectation{
 		check:       check,
-		description: "empty diagnostics",
+		description: "no diagnostics",
 	}
 }