diff --git a/http2/single_use_test.go b/http2/single_use_test.go
new file mode 100644
index 00000000..82fa136e
--- /dev/null
+++ b/http2/single_use_test.go
@@ -0,0 +1,99 @@
+package http2_test
+
+import (
+	"io"
+	"net"
+	stdhttp "net/http"
+	stdhttptest "net/http/httptest"
+	"sync/atomic"
+	"testing"
+	"time"
+
+	http "github.com/bogdanfinn/fhttp"
+	"github.com/bogdanfinn/fhttp/http2"
+	tls "github.com/bogdanfinn/utls"
+)
+
+// A Connection: close request gets a single-use connection. That connection
+// used to count as spent as soon as its next stream id passed 1, which is
+// already true before any request when the first stream is not 1, as with
+// InitialStreamID or PRIORITY frames. The request was then never sent and the
+// transport dialed a new connection over and over.
+func TestSingleUseConnServesItsRequestWhenTheFirstStreamIsNotOne(t *testing.T) {
+	cases := []struct {
+		name      string
+		configure func(*http2.Transport)
+		close     bool
+	}{
+		{name: "first stream 1, Connection: close", close: true},
+		{name: "InitialStreamID 3, keep-alive", configure: func(tr *http2.Transport) { tr.InitialStreamID = 3 }},
+		{name: "InitialStreamID 3, Connection: close", configure: func(tr *http2.Transport) { tr.InitialStreamID = 3 }, close: true},
+		{name: "PRIORITY frames, Connection: close", configure: func(tr *http2.Transport) {
+			tr.Priorities = []http2.Priority{
+				{StreamID: 3, PriorityParam: http2.PriorityParam{Weight: 200}},
+				{StreamID: 5, PriorityParam: http2.PriorityParam{Weight: 100}},
+			}
+		}, close: true},
+	}
+
+	for _, c := range cases {
+		t.Run(c.name, func(t *testing.T) {
+			var conns atomic.Int32
+			srv := stdhttptest.NewUnstartedServer(stdhttp.HandlerFunc(func(w stdhttp.ResponseWriter, r *stdhttp.Request) {
+				io.WriteString(w, r.Proto)
+			}))
+			srv.EnableHTTP2 = true
+			srv.Config.ConnState = func(_ net.Conn, s stdhttp.ConnState) {
+				if s == stdhttp.StateNew {
+					conns.Add(1)
+				}
+			}
+			srv.StartTLS()
+			defer srv.Close()
+
+			tr := &http2.Transport{TLSClientConfig: &tls.Config{InsecureSkipVerify: true}}
+			if c.configure != nil {
+				c.configure(tr)
+			}
+			defer tr.CloseIdleConnections()
+
+			req, err := http.NewRequest(http.MethodGet, srv.URL, nil)
+			if err != nil {
+				t.Fatal(err)
+			}
+			req.Close = c.close
+
+			type result struct {
+				body string
+				err  error
+			}
+			done := make(chan result, 1)
+			go func() {
+				res, err := tr.RoundTrip(req)
+				if err != nil {
+					done <- result{err: err}
+					return
+				}
+				defer res.Body.Close()
+				b, err := io.ReadAll(res.Body)
+				done <- result{body: string(b), err: err}
+			}()
+
+			select {
+			case r := <-done:
+				if r.err != nil {
+					t.Fatalf("round trip: %v", r.err)
+				}
+				if r.body != "HTTP/2.0" {
+					t.Fatalf("body = %q, want HTTP/2.0", r.body)
+				}
+			case <-time.After(5 * time.Second):
+				t.Fatalf("no response after 5s, %d connections dialed", conns.Load())
+			}
+
+			if n := conns.Load(); n != 1 {
+				t.Fatalf("dialed %d connections for one request, want 1", n)
+			}
+		})
+	}
+}
diff --git a/http2/transport.go b/http2/transport.go
index 74b7adbd..b3d56f30 100644
--- a/http2/transport.go
+++ b/http2/transport.go
@@ -339,6 +339,7 @@ type ClientConn struct {
 
 	mu                    sync.Mutex // guards following
 	nextStreamID          uint32
+	firstStreamID         uint32 // nextStreamID before any request: 1 unless InitialStreamID, AllowHTTP or Priorities moved it
 	peerMaxHeaderListSize uint64
 	pendingRequests       int                       // requests blocked and waiting to be sent because len(streams) == maxConcurrentStreams
 	pings                 map[[8]byte]chan struct{} // in flight ping data to notification channel
@@ -886,6 +887,11 @@ func (t *Transport) newClientConn(c net.Conn, addr string, singleUse bool) (*Cli
 		cc.nextStreamID = priority.StreamID + 2
 	}
 
+	// The first stream is not always 1, so remember where this connection
+	// starts. idleStateLocked uses it to tell an unused connection from a
+	// used one.
+	cc.firstStreamID = cc.nextStreamID
+
 	// Use the dynamic connection flow value we calculated earlier
 	cc.inflow.add(int32(cc.connFlow) + int32(initialWindowSize))
 
@@ -964,7 +970,7 @@ func (cc *ClientConn) idleState() clientConnIdleState {
 }
 
 func (cc *ClientConn) idleStateLocked() (st clientConnIdleState) {
-	if cc.singleUse && cc.nextStreamID > 1 {
+	if cc.singleUse && cc.nextStreamID > cc.firstStreamID {
 		return
 	}
 	var maxConcurrentOkay bool
@@ -981,7 +987,7 @@ func (cc *ClientConn) idleStateLocked() (st clientConnIdleState) {
 	st.canTakeNewRequest = cc.goAway == nil && !cc.closed && !cc.closing && maxConcurrentOkay &&
 		int64(cc.nextStreamID)+2*int64(cc.pendingRequests) < math.MaxInt32 &&
 		!cc.tooIdleLocked()
-	st.freshConn = cc.nextStreamID == 1 && st.canTakeNewRequest
+	st.freshConn = cc.nextStreamID == cc.firstStreamID && st.canTakeNewRequest
 
 	return
 }