diff --git a/main.go b/main.go
index 3c6ea74..a0599a2 100644
--- a/main.go
+++ b/main.go
@@ -1,4 +1,4 @@
-// Copyright 2019, 2021 The Alpaca Authors
+// Copyright 2019, 2021, 2022 The Alpaca Authors
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -87,7 +87,7 @@ func main() {
 
 	pacWrapper := NewPACWrapper(PACData{Port: *port})
 	proxyFinder := NewProxyFinder(pacURL, pacWrapper)
-	proxyHandler := NewProxyHandler(proxyFinder.findProxyForRequest, a, proxyFinder.blockProxy)
+	proxyHandler := NewProxyHandler(a, getProxyFromContext, proxyFinder.blockProxy)
 	mux := http.NewServeMux()
 	pacWrapper.SetupHandlers(mux)
 
diff --git a/proxy.go b/proxy.go
index e71990f..76819d5 100644
--- a/proxy.go
+++ b/proxy.go
@@ -1,4 +1,4 @@
-// Copyright 2019, 2021 The Alpaca Authors
+// Copyright 2019, 2021, 2022 The Alpaca Authors
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -37,7 +37,7 @@ type ProxyHandler struct {
 
 type proxyFunc func(*http.Request) (*url.URL, error)
 
-func NewProxyHandler(proxy proxyFunc, auth *authenticator, block func(string)) ProxyHandler {
+func NewProxyHandler(auth *authenticator, proxy proxyFunc, block func(string)) ProxyHandler {
 	return ProxyHandler{&http.Transport{Proxy: proxy}, auth, block}
 }
 
@@ -69,22 +69,20 @@ func (ph ProxyHandler) ServeHTTP(w http.ResponseWriter, req *http.Request) {
 
 func (ph ProxyHandler) handleConnect(w http.ResponseWriter, req *http.Request) {
 	// Establish a connection to the server, or an upstream proxy.
-	u, err := ph.transport.Proxy(req)
 	id := req.Context().Value(contextKeyID)
+	proxy, err := ph.transport.Proxy(req)
 	if err != nil {
-		log.Printf("[%d] Error finding proxy for %v: %v", id, req.Host, err)
-		w.WriteHeader(http.StatusInternalServerError)
-		return
+		log.Printf("[%d] Error finding proxy for request: %v", id, err)
 	}
 	var server net.Conn
-	if u == nil {
-		server, err = net.Dial("tcp", req.Host)
+	if proxy == nil {
+		server, err = connectDirect(req)
 	} else {
-		server, err = connectViaProxy(req, u.Host, ph.auth)
+		server, err = connectViaProxy(req, proxy.Host, ph.auth)
 		var dialErr *dialError
 		if errors.As(err, &dialErr) {
-			log.Printf("[%d] Temporarily blocking unreachable proxy: %q", id, u.Host)
-			ph.block(u.Host)
+			log.Printf("[%d] Temporarily blocking proxy: %q", id, proxy.Host)
+			ph.block(proxy.Host)
 		}
 	}
 	if err != nil {
@@ -130,12 +128,21 @@ func (ph ProxyHandler) handleConnect(w http.ResponseWriter, req *http.Request) {
 	go func() { _, _ = io.Copy(client, server); client.Close() }()
 }
 
+func connectDirect(req *http.Request) (net.Conn, error) {
+	server, err := net.Dial("tcp", req.Host)
+	if err != nil {
+		id := req.Context().Value(contextKeyID)
+		log.Printf("[%d] Error dialling host %s: %v", id, req.Host, err)
+	}
+	return server, err
+}
+
 func connectViaProxy(req *http.Request, proxy string, auth *authenticator) (net.Conn, error) {
 	id := req.Context().Value(contextKeyID)
 	var tr transport
 	defer tr.Close()
 	if err := tr.dial("tcp", proxy); err != nil {
-		log.Printf("[%d] Error dialling %s: %v", id, proxy, err)
+		log.Printf("[%d] Error dialling proxy %s: %v", id, proxy, err)
 		return nil, err
 	}
 	resp, err := tr.RoundTrip(req)
@@ -176,7 +183,7 @@ func (ph ProxyHandler) proxyRequest(w http.ResponseWriter, req *http.Request, au
 	resp, err := ph.transport.RoundTrip(req)
 	if err != nil {
 		log.Printf("[%d] Error forwarding request: %v", id, err)
-		w.WriteHeader(http.StatusInternalServerError)
+		w.WriteHeader(http.StatusBadGateway)
 		var dialErr *dialError
 		if errors.As(err, &dialErr) && dialErr.address != req.Host {
 			log.Printf("[%d] Temporarily blocking unreachable proxy: %q",
@@ -196,7 +203,7 @@ func (ph ProxyHandler) proxyRequest(w http.ResponseWriter, req *http.Request, au
 			resp, err = auth.do(req, ph.transport)
 			if err != nil {
 				log.Printf("[%d] Error forwarding request (with auth): %v", id, err)
-				w.WriteHeader(http.StatusInternalServerError)
+				w.WriteHeader(http.StatusBadGateway)
 				return
 			}
 			defer resp.Body.Close()
diff --git a/proxy_test.go b/proxy_test.go
index fd7d1d0..c9d860c 100644
--- a/proxy_test.go
+++ b/proxy_test.go
@@ -1,4 +1,4 @@
-// Copyright 2019 The Alpaca Authors
+// Copyright 2019, 2021, 2022 The Alpaca Authors
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -16,6 +16,7 @@ package main
 
 import (
 	"bufio"
+	"context"
 	"crypto/tls"
 	"crypto/x509"
 	"fmt"
@@ -54,17 +55,17 @@ func (tp testProxy) ServeHTTP(w http.ResponseWriter, req *http.Request) {
 }
 
 func newDirectProxy() ProxyHandler {
-	return NewProxyHandler(
-		func(r *http.Request) (*url.URL, error) { return nil, nil },
-		nil,
-		func(string) {},
-	)
+	return NewProxyHandler(nil, http.ProxyURL(nil), func(string) {})
 }
 
-func newChildProxy(parent *httptest.Server) ProxyHandler {
-	return NewProxyHandler(func(r *http.Request) (*url.URL, error) {
-		return &url.URL{Host: parent.Listener.Addr().String()}, nil
-	}, nil, func(string) {})
+func newChildProxy(parent *httptest.Server) http.Handler {
+	parentURL := &url.URL{Host: parent.Listener.Addr().String()}
+	childProxy := NewProxyHandler(nil, getProxyFromContext, func(string) {})
+	return http.HandlerFunc(func(w http.ResponseWriter, req *http.Request) {
+		ctx := context.WithValue(req.Context(), contextKeyProxy, parentURL)
+		reqWithProxy := req.WithContext(ctx)
+		childProxy.ServeHTTP(w, reqWithProxy)
+	})
 }
 
 func proxyServer(t *testing.T, proxy *httptest.Server) proxyFunc {
@@ -336,3 +337,11 @@ func TestConnectResponseHasCorrectNewlines(t *testing.T) {
 	assert.NotContains(t, noCRLFs, "\r", "response contains unmatched CR")
 	assert.NotContains(t, noCRLFs, "\n", "response contains unmatched LF")
 }
+
+func TestConnectToNonExistentHost(t *testing.T) {
+	proxy := httptest.NewServer(newDirectProxy())
+	defer proxy.Close()
+	client := http.Client{Transport: &http.Transport{Proxy: proxyServer(t, proxy)}}
+	_, err := client.Get("https://nonexistent.test")
+	require.Error(t, err)
+}
diff --git a/proxyfinder.go b/proxyfinder.go
index 2f45901..2d99185 100644
--- a/proxyfinder.go
+++ b/proxyfinder.go
@@ -1,4 +1,4 @@
-// Copyright 2019, 2021 The Alpaca Authors
+// Copyright 2019, 2021, 2022 The Alpaca Authors
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -15,6 +15,7 @@
 package main
 
 import (
+	"context"
 	"errors"
 	"log"
 	"net"
@@ -24,6 +25,16 @@ import (
 	"sync"
 )
 
+const contextKeyProxy = contextKey("proxy")
+
+func getProxyFromContext(req *http.Request) (*url.URL, error) {
+	if value := req.Context().Value(contextKeyProxy); value != nil {
+		proxy := value.(*url.URL)
+		return proxy, nil
+	}
+	return nil, nil
+}
+
 type ProxyFinder struct {
 	runner  *PACRunner
 	fetcher *pacFetcher
@@ -53,7 +64,14 @@ func (pf *ProxyFinder) WrapHandler(next http.Handler) http.Handler {
 	}
 	return http.HandlerFunc(func(w http.ResponseWriter, req *http.Request) {
 		pf.checkForUpdates()
-		next.ServeHTTP(w, req)
+		proxy, err := pf.findProxyForRequest(req)
+		if err != nil {
+			log.Printf("[%d] %v", req.Context().Value(contextKeyID), err)
+			w.WriteHeader(http.StatusInternalServerError)
+			return
+		}
+		ctx := context.WithValue(req.Context(), contextKeyProxy, proxy)
+		next.ServeHTTP(w, req.WithContext(ctx))
 	})
 }