diff --git a/cleanhttp.go b/cleanhttp.go
index 20d1c0a..68567bf 100644
--- a/cleanhttp.go
+++ b/cleanhttp.go
@@ -13,7 +13,7 @@ import (
 // DefaultTransport returns a new http.Transport with similar default values to
 // http.DefaultTransport, but with idle connections and keepalives disabled.
 func DefaultTransport() *http.Transport {
-	transport := DefaultPooledTransport()
+	transport := DefaultPooledTransportWithMin(0)
 	transport.DisableKeepAlives = true
 	transport.MaxIdleConnsPerHost = -1
 	return transport
@@ -24,6 +24,14 @@ func DefaultTransport() *http.Transport {
 // it can leak file descriptors over time. Only use this for transports that
 // will be re-used for the same host(s).
 func DefaultPooledTransport() *http.Transport {
+	return DefaultPooledTransportWithMin(0)
+}
+
+// DefaultPooledTransportWithMin returns a new http.Transport with a minimum
+// value for MaxIdleConnsPerHost. Do not use this for transient transports as
+// it can leak file descriptors over time. Only use this for transports that
+// will be re-used for the same host(s).
+func DefaultPooledTransportWithMin(minIdleConnsPerHost int) *http.Transport {
 	transport := &http.Transport{
 		Proxy: http.ProxyFromEnvironment,
 		DialContext: (&net.Dialer{
@@ -36,7 +44,13 @@ func DefaultPooledTransport() *http.Transport {
 		TLSHandshakeTimeout:   10 * time.Second,
 		ExpectContinueTimeout: 1 * time.Second,
 		ForceAttemptHTTP2:     true,
-		MaxIdleConnsPerHost:   runtime.GOMAXPROCS(0) + 1,
+		MaxIdleConnsPerHost: func() int {
+			maxIdleConnsPerHost := runtime.GOMAXPROCS(0) + 1
+			if maxIdleConnsPerHost < minIdleConnsPerHost {
+				return minIdleConnsPerHost
+			}
+			return maxIdleConnsPerHost
+		}(),
 	}
 	return transport
 }
@@ -55,7 +69,15 @@ func DefaultClient() *http.Client {
 // transient clients as it can leak file descriptors over time. Only use this
 // for clients that will be re-used for the same host(s).
 func DefaultPooledClient() *http.Client {
+	return DefaultPooledClientWithMin(0)
+}
+
+// DefaultPooledClient returns a new http.Client with similar default values to
+// http.Client, but with a shared Transport and minimum value for MaxIdleConnsPerHost.
+// Do not use this function for transient clients as it can leak file descriptors
+// over time. Only use this for clients that will be re-used for the same host(s).
+func DefaultPooledClientWithMin(minIdleConnsPerHost int) *http.Client {
 	return &http.Client{
-		Transport: DefaultPooledTransport(),
+		Transport: DefaultPooledTransportWithMin(minIdleConnsPerHost),
 	}
 }