diff --git a/internal/lsp/lsp_test.go b/internal/lsp/lsp_test.go
index 800c5e9..386e5e8 100644
--- a/internal/lsp/lsp_test.go
+++ b/internal/lsp/lsp_test.go
@@ -20,6 +20,7 @@
 	"golang.org/x/tools/internal/lsp/diff"
 	"golang.org/x/tools/internal/lsp/protocol"
 	"golang.org/x/tools/internal/lsp/source"
+	"golang.org/x/tools/internal/lsp/telemetry/log"
 	"golang.org/x/tools/internal/lsp/tests"
 	"golang.org/x/tools/internal/span"
 )
@@ -41,6 +42,8 @@
 	data := tests.Load(t, exporter, "testdata")
 	defer data.Exported.Cleanup()
 
+	log.AddLogger(log.NullLogger)
+
 	cache := cache.New()
 	session := cache.NewSession(ctx)
 	view := session.NewView(ctx, viewName, span.FileURI(data.Config.Dir))
diff --git a/internal/lsp/source/deep_completion.go b/internal/lsp/source/deep_completion.go
index bb1fbbf..7d2f6ad 100644
--- a/internal/lsp/source/deep_completion.go
+++ b/internal/lsp/source/deep_completion.go
@@ -56,6 +56,12 @@
 		return
 	}
 
+	// If we are definitely completing a struct field name, deep completions
+	// don't make sense.
+	if c.wantStructFieldCompletions() && c.enclosingCompositeLiteral.inKey {
+		return
+	}
+
 	// Don't search into type names.
 	if isTypeName(obj) {
 		return
diff --git a/internal/lsp/source/source_test.go b/internal/lsp/source/source_test.go
index b54684d..1de9474 100644
--- a/internal/lsp/source/source_test.go
+++ b/internal/lsp/source/source_test.go
@@ -18,6 +18,7 @@
 	"golang.org/x/tools/internal/lsp/cache"
 	"golang.org/x/tools/internal/lsp/diff"
 	"golang.org/x/tools/internal/lsp/source"
+	"golang.org/x/tools/internal/lsp/telemetry/log"
 	"golang.org/x/tools/internal/lsp/tests"
 	"golang.org/x/tools/internal/span"
 )
@@ -37,6 +38,8 @@
 	data := tests.Load(t, exporter, "../testdata")
 	defer data.Exported.Cleanup()
 
+	log.AddLogger(log.NullLogger)
+
 	cache := cache.New()
 	session := cache.NewSession(ctx)
 	r := &runner{
diff --git a/internal/lsp/telemetry/log/log.go b/internal/lsp/telemetry/log/log.go
index 8391ad7..2d957f6 100644
--- a/internal/lsp/telemetry/log/log.go
+++ b/internal/lsp/telemetry/log/log.go
@@ -90,3 +90,9 @@
 	fmt.Fprintf(os.Stderr, "%v\n", ToEntry(ctx, at, tags))
 	return true
 }
+
+// NullLogger is a logger that throws away log messages and reports
+// success so that the fallback stderr logging does not happen.
+var NullLogger = func(context.Context, time.Time, tag.List) bool {
+	return true
+}
diff --git a/internal/lsp/testdata/deepcomplete/deep_complete.go b/internal/lsp/testdata/deepcomplete/deep_complete.go
index bfde660..2f31b1f 100644
--- a/internal/lsp/testdata/deepcomplete/deep_complete.go
+++ b/internal/lsp/testdata/deepcomplete/deep_complete.go
@@ -59,3 +59,14 @@
 	a.deepEmbedC     //@item(deepEmbedC, "a.deepEmbedC", "deepEmbedC", "field")
 	wantsC(a)        //@complete(")", deepEmbedC, deepEmbedA, deepEmbedB)
 }
+
+func _() {
+	type nested struct {
+		a int
+		n *nested //@item(deepNestedField, "n", "*nested", "field")
+	}
+
+	nested{
+		a: 123, //@complete(" //", deepNestedField)
+	}
+}
diff --git a/internal/lsp/tests/tests.go b/internal/lsp/tests/tests.go
index 88fb2c3..608cd3f 100644
--- a/internal/lsp/tests/tests.go
+++ b/internal/lsp/tests/tests.go
@@ -26,7 +26,7 @@
 // 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       = 144
+	ExpectedCompletionsCount       = 145
 	ExpectedCompletionSnippetCount = 15
 	ExpectedDiagnosticsCount       = 21
 	ExpectedFormatCount            = 6
@@ -195,12 +195,12 @@
 		filename := data.Exported.File(testModule, fragment)
 		data.fragments[filename] = fragment
 	}
-	data.Exported.Config.Logf = t.Logf
+	data.Exported.Config.Logf = nil
 
 	// Merge the exported.Config with the view.Config.
 	data.Config = *data.Exported.Config
 	data.Config.Fset = token.NewFileSet()
-	data.Config.Logf = t.Logf
+	data.Config.Logf = nil
 	data.Config.Context = Context(nil)
 	data.Config.ParseFile = func(fset *token.FileSet, filename string, src []byte) (*ast.File, error) {
 		panic("ParseFile should not be called")