diff --git a/internal/config/concurrency_limits_internal_test.go b/internal/config/concurrency_limits_internal_test.go
index 9639bdc..33634a4 100644
--- a/internal/config/concurrency_limits_internal_test.go
+++ b/internal/config/concurrency_limits_internal_test.go
@@ -33,6 +33,35 @@ func TestOmittedConcurrencyLimitsUseDefaults(t *testing.T) {
 	}
 }
 
+// TestOmittedMaxConcurrentProcessingIsHalfTheCPUsAndAtLeastOne checks
+// that an omitted max_concurrent_processing is half the CPUs Go uses,
+// rounded down, and 1 when Go uses one CPU.
+//
+//nolint:paralleltest // it sets GOMAXPROCS, which other tests read
+func TestOmittedMaxConcurrentProcessingIsHalfTheCPUsAndAtLeastOne(t *testing.T) {
+	cpusBefore := runtime.GOMAXPROCS(0)
+	t.Cleanup(func() { runtime.GOMAXPROCS(cpusBefore) })
+
+	for _, tc := range []struct{ cpus, want int }{
+		{1, 1}, {2, 1}, {3, 1}, {8, 4},
+	} {
+		runtime.GOMAXPROCS(tc.cpus)
+
+		c, err := configFromYAML(t, signingKeyLine)
+		if err != nil {
+			t.Fatalf("minimal config should be valid, got error: %v", err)
+		}
+
+		t.Logf("GOMAXPROCS %d: MaxConcurrentProcessing %d",
+			tc.cpus, c.MaxConcurrentProcessing)
+
+		if c.MaxConcurrentProcessing != tc.want {
+			t.Errorf("GOMAXPROCS %d: MaxConcurrentProcessing = %d, want %d",
+				tc.cpus, c.MaxConcurrentProcessing, tc.want)
+		}
+	}
+}
+
 // TestExplicitConcurrencyLimitsAreUsed checks that valid values for the
 // two limits are used as given.
 func TestExplicitConcurrencyLimitsAreUsed(t *testing.T) {
diff --git a/internal/imageprocessor/max_concurrent_processing_internal_test.go b/internal/imageprocessor/max_concurrent_processing_internal_test.go
index ba5388c..a174752 100644
--- a/internal/imageprocessor/max_concurrent_processing_internal_test.go
+++ b/internal/imageprocessor/max_concurrent_processing_internal_test.go
@@ -132,6 +132,29 @@ func TestNewDefaultsMaxConcurrentProcessingToCPUs(t *testing.T) {
 	}
 }
 
+// TestNewDefaultIsHalfTheCPUsAndAtLeastOne checks that New, given no
+// MaxConcurrentProcessing, makes one slot for every two CPUs Go uses,
+// rounded down, and one slot when Go uses one CPU.
+//
+//nolint:paralleltest // it sets GOMAXPROCS, which other tests read
+func TestNewDefaultIsHalfTheCPUsAndAtLeastOne(t *testing.T) {
+	cpusBefore := runtime.GOMAXPROCS(0)
+	t.Cleanup(func() { runtime.GOMAXPROCS(cpusBefore) })
+
+	for _, tc := range []struct{ cpus, want int }{
+		{1, 1}, {2, 1}, {3, 1}, {8, 4},
+	} {
+		runtime.GOMAXPROCS(tc.cpus)
+
+		got := cap(New(Params{}).processingSemaphore)
+		t.Logf("GOMAXPROCS %d: %d slots", tc.cpus, got)
+
+		if got != tc.want {
+			t.Errorf("GOMAXPROCS %d: %d slots, want %d", tc.cpus, got, tc.want)
+		}
+	}
+}
+
 // TestProcessNeverExceedsMaxConcurrentProcessing starts more Process calls
 // than MaxConcurrentProcessing allows and holds the first ones inside
 // Process until the test lets them go. No more than the limit may be