diff --git a/src/cmd/go/testdata/script/test_fuzz_fuzztime.txt b/src/cmd/go/testdata/script/test_fuzz_fuzztime.txt
index 7d644b4..9c9972f 100644
--- a/src/cmd/go/testdata/script/test_fuzz_fuzztime.txt
+++ b/src/cmd/go/testdata/script/test_fuzz_fuzztime.txt
@@ -16,13 +16,24 @@
 # Timeout should not cause inputs to be written as crashers.
 ! exists testdata/fuzz
 
-# When we use fuzztime with an "x" suffix, it runs a specific number of times.
-# This fuzz function creates a file with a unique name ($pid.$count) on each run.
-# We count the files to find the number of runs.
-mkdir count
 env GOCACHE=$WORK/tmp
-go test -fuzz=FuzzCount -fuzztime=1000x -fuzzminimizetime=1x
-go run check_file_count.go 1000
+
+# When we use fuzztime with an "x" suffix, it runs a specific number of times.
+# This fuzz function creates a file with a unique name ($pid.$count) on each
+# run. We count the files to find the number of runs.
+mkdir count
+go test -fuzz=FuzzTestCount -fuzztime=1000x -fuzzminimizetime=1x
+go run check_file_count.go count 1000
+
+# When we use fuzzminimizetime with an "x" suffix, it runs a specific number of
+# times while minimizing. This fuzz function creates a file with a unique name
+# ($pid.$count) on each run once the first crash has been found. That means that
+# there should be one file for each execution of the fuzz function during
+# minimization, so we count these to determine how many times minimization was
+# run.
+mkdir minimizecount
+! go test -fuzz=FuzzMinimizeCount -fuzzminimizetime=3x -parallel=1
+go run check_file_count.go minimizecount 3
 
 -- go.mod --
 module fuzz
@@ -45,7 +56,7 @@
 	"testing"
 )
 
-func FuzzCount(f *testing.F) {
+func FuzzTestCount(f *testing.F) {
 	pid := os.Getpid()
 	n := 0
 	f.Fuzz(func(t *testing.T, _ []byte) {
@@ -56,6 +67,36 @@
 		n++
 	})
 }
+-- fuzz_minimize_count_test.go --
+package fuzz
+
+import (
+	"bytes"
+	"fmt"
+	"os"
+	"testing"
+)
+
+func FuzzMinimizeCount(f *testing.F) {
+	pid := os.Getpid()
+	n := 0
+	seed := bytes.Repeat([]byte("a"), 357)
+	f.Add(seed)
+	crashFound := false
+	f.Fuzz(func(t *testing.T, b []byte) {
+		if crashFound {
+			name := fmt.Sprintf("minimizecount/%v.%d", pid, n)
+			if err := os.WriteFile(name, nil, 0666); err != nil {
+				t.Fatal(err)
+			}
+			n++
+		}
+		if !bytes.Equal(b, seed) {  // this should happen right away
+			crashFound = true
+			t.Error("minimize this!")
+		}
+	})
+}
 -- check_file_count.go --
 // +build ignore
 
@@ -68,13 +109,13 @@
 )
 
 func main() {
-	dir, err := os.ReadDir("count")
+	dir, err := os.ReadDir(os.Args[1])
 	if err != nil {
 		fmt.Fprintln(os.Stderr, err)
 		os.Exit(1)
 	}
 	got := len(dir)
-	want, _ := strconv.Atoi(os.Args[1])
+	want, _ := strconv.Atoi(os.Args[2])
 	if got != want {
 		fmt.Fprintf(os.Stderr, "got %d files; want %d\n", got, want)
 		os.Exit(1)
diff --git a/src/internal/fuzz/fuzz.go b/src/internal/fuzz/fuzz.go
index a8bbd60..03071d5 100644
--- a/src/internal/fuzz/fuzz.go
+++ b/src/internal/fuzz/fuzz.go
@@ -825,9 +825,11 @@
 			}
 		}
 	}
-	remaining := c.opts.Limit - c.count - c.countWaiting
-	if input.limit > remaining {
-		input.limit = remaining
+	if c.opts.Limit > 0 {
+		remaining := c.opts.Limit - c.count - c.countWaiting
+		if input.limit > remaining {
+			input.limit = remaining
+		}
 	}
 	return input, true
 }