diff --git a/net/dns/resolver/forwarder.go b/net/dns/resolver/forwarder.go
index 557f4522f..2069af95c 100644
--- a/net/dns/resolver/forwarder.go
+++ b/net/dns/resolver/forwarder.go
@@ -16,6 +16,7 @@ import (
 	"math/rand"
 	"net"
 	"net/http"
+	"runtime"
 	"strings"
 	"sync"
 	"time"
@@ -159,6 +160,7 @@ type forwarder struct {
 	logf    logger.Logf
 	linkMon *monitor.Mon
 	linkSel ForwardLinkSelector
+	dohSem  chan struct{}
 
 	ctx       context.Context    // good until Close
 	ctxCancel context.CancelFunc // closes ctx
@@ -180,11 +182,18 @@ func init() {
 }
 
 func newForwarder(logf logger.Logf, responses chan packet, linkMon *monitor.Mon, linkSel ForwardLinkSelector) *forwarder {
+	maxDoHInFlight := 1000 // effectively unlimited
+	if runtime.GOOS == "ios" {
+		// No HTTP/2 on iOS yet (for size reasons), so DoH is
+		// pricier.
+		maxDoHInFlight = 10
+	}
 	f := &forwarder{
 		logf:      logger.WithPrefix(logf, "forward: "),
 		linkMon:   linkMon,
 		linkSel:   linkSel,
 		responses: responses,
+		dohSem:    make(chan struct{}, maxDoHInFlight),
 	}
 	f.ctx, f.ctxCancel = context.WithCancel(context.Background())
 	return f
@@ -262,7 +271,22 @@ func (f *forwarder) getDoHClient(ip netaddr.IP) (urlBase string, c *http.Client,
 
 const dohType = "application/dns-message"
 
+func (f *forwarder) releaseDoHSem() { <-f.dohSem }
+
 func (f *forwarder) sendDoH(ctx context.Context, urlBase string, c *http.Client, packet []byte) ([]byte, error) {
+	// Bound the number of HTTP requests in flight. This primarily
+	// matters for iOS where we're very memory constrained and
+	// HTTP requests are heavier on iOS where we don't include
+	// HTTP/2 for binary size reasons (as binaries on iOS linked
+	// with Go code cost memory proportional to the binary size,
+	// for reasons not fully understood).
+	select {
+	case f.dohSem <- struct{}{}:
+	case <-ctx.Done():
+		return nil, ctx.Err()
+	}
+	defer f.releaseDoHSem()
+
 	req, err := http.NewRequestWithContext(ctx, "POST", urlBase, bytes.NewReader(packet))
 	if err != nil {
 		return nil, err