diff --git a/internal/lsp/completion_test.go b/internal/lsp/completion_test.go
index 022468adc0..7c20ce103a 100644
--- a/internal/lsp/completion_test.go
+++ b/internal/lsp/completion_test.go
@@ -3,7 +3,6 @@ package lsp
 import (
 	"strings"
 	"testing"
-	"time"
 
 	"golang.org/x/tools/internal/lsp/protocol"
 	"golang.org/x/tools/internal/lsp/source"
@@ -30,7 +29,6 @@ func (r *runner) CompletionSnippet(t *testing.T, src span.Span, expected tests.C
 	list := r.callCompletion(t, src, source.CompletionOptions{
 		Placeholders:  placeholders,
 		Deep:          true,
-		Budget:        5 * time.Second,
 		FuzzyMatching: true,
 	})
 	got := tests.FindItem(list, *items[expected.CompletionItem])
@@ -59,7 +57,6 @@ func (r *runner) UnimportedCompletion(t *testing.T, src span.Span, test tests.Co
 func (r *runner) DeepCompletion(t *testing.T, src span.Span, test tests.Completion, items tests.CompletionItems) {
 	got := r.callCompletion(t, src, source.CompletionOptions{
 		Deep:          true,
-		Budget:        5 * time.Second,
 		Documentation: true,
 	})
 	if !strings.Contains(string(src.URI()), "builtins") {
@@ -75,7 +72,6 @@ func (r *runner) FuzzyCompletion(t *testing.T, src span.Span, test tests.Complet
 	got := r.callCompletion(t, src, source.CompletionOptions{
 		FuzzyMatching: true,
 		Deep:          true,
-		Budget:        5 * time.Second,
 	})
 	if !strings.Contains(string(src.URI()), "builtins") {
 		got = tests.FilterBuiltins(got)
@@ -103,7 +99,6 @@ func (r *runner) RankCompletion(t *testing.T, src span.Span, test tests.Completi
 	got := r.callCompletion(t, src, source.CompletionOptions{
 		FuzzyMatching: true,
 		Deep:          true,
-		Budget:        5 * time.Second,
 	})
 	want := expected(t, test, items)
 	if msg := tests.CheckCompletionOrder(want, got); msg != "" {
@@ -121,6 +116,7 @@ func expected(t *testing.T, test tests.Completion, items tests.CompletionItems)
 	}
 	return want
 }
+
 func (r *runner) callCompletion(t *testing.T, src span.Span, options source.CompletionOptions) []protocol.CompletionItem {
 	t.Helper()
 
diff --git a/internal/lsp/source/deep_completion.go b/internal/lsp/source/deep_completion.go
index 6dd85e7026..b175933879 100644
--- a/internal/lsp/source/deep_completion.go
+++ b/internal/lsp/source/deep_completion.go
@@ -107,7 +107,7 @@ func (c *completer) shouldPrune() bool {
 	}
 
 	// Check our remaining budget every 100 candidates.
-	if c.deepState.candidateCount%100 == 0 {
+	if c.opts.Budget > 0 && c.deepState.candidateCount%100 == 0 {
 		spent := float64(time.Since(c.startTime)) / float64(c.opts.Budget)
 
 		switch {
diff --git a/internal/lsp/source/options.go b/internal/lsp/source/options.go
index e1bc782b90..6f02651f52 100644
--- a/internal/lsp/source/options.go
+++ b/internal/lsp/source/options.go
@@ -119,7 +119,7 @@ type CompletionOptions struct {
 	// requests finish in a couple milliseconds, but in some cases deep
 	// completions can take much longer. As we use up our budget we
 	// dynamically reduce the search scope to ensure we return timely
-	// results.
+	// results. Zero means unlimited.
 	Budget time.Duration
 }
 
diff --git a/internal/lsp/source/source_test.go b/internal/lsp/source/source_test.go
index 8c0d19e7dc..c85cdd8e9d 100644
--- a/internal/lsp/source/source_test.go
+++ b/internal/lsp/source/source_test.go
@@ -14,7 +14,6 @@ import (
 	"sort"
 	"strings"
 	"testing"
-	"time"
 
 	"golang.org/x/tools/go/packages/packagestest"
 	"golang.org/x/tools/internal/lsp/cache"
@@ -113,7 +112,6 @@ func (r *runner) CompletionSnippet(t *testing.T, src span.Span, expected tests.C
 	_, list := r.callCompletion(t, src, source.CompletionOptions{
 		Placeholders: placeholders,
 		Deep:         true,
-		Budget:       5 * time.Second,
 	})
 	got := tests.FindItem(list, *items[expected.CompletionItem])
 	want := expected.PlainSnippet
@@ -148,7 +146,6 @@ func (r *runner) DeepCompletion(t *testing.T, src span.Span, test tests.Completi
 	}
 	prefix, list := r.callCompletion(t, src, source.CompletionOptions{
 		Deep:          true,
-		Budget:        5 * time.Second,
 		Documentation: true,
 	})
 	if !strings.Contains(string(src.URI()), "builtins") {
@@ -175,7 +172,6 @@ func (r *runner) FuzzyCompletion(t *testing.T, src span.Span, test tests.Complet
 	prefix, list := r.callCompletion(t, src, source.CompletionOptions{
 		FuzzyMatching: true,
 		Deep:          true,
-		Budget:        5 * time.Second,
 	})
 	if !strings.Contains(string(src.URI()), "builtins") {
 		list = tests.FilterBuiltins(list)
@@ -220,7 +216,6 @@ func (r *runner) RankCompletion(t *testing.T, src span.Span, test tests.Completi
 	prefix, list := r.callCompletion(t, src, source.CompletionOptions{
 		FuzzyMatching: true,
 		Deep:          true,
-		Budget:        5 * time.Second,
 	})
 	fuzzyMatcher := fuzzy.NewMatcher(prefix)
 	var got []protocol.CompletionItem