diff --git a/be_misc.c b/be_misc.c
index 84d24639..9bd3bdd3 100644
--- a/be_misc.c
+++ b/be_misc.c
@@ -59,12 +59,15 @@ void backend_socket_log(Seat *seat, LogContext *logctx,
     }
 }
 
-void log_proxy_stderr(Plug *plug, bufchain *buf, const void *vdata, size_t len)
+void psb_init(ProxyStderrBuf *psb)
+{
+    psb->size = 0;
+}
+
+void log_proxy_stderr(Plug *plug, ProxyStderrBuf *psb,
+                      const void *vdata, size_t len)
 {
     const char *data = (const char *)vdata;
-    size_t pos = 0;
-    const char *nlpos;
-    char *msg, *fullmsg;
 
     /*
      * This helper function allows us to collect the data written to a
@@ -72,43 +75,77 @@ void log_proxy_stderr(Plug *plug, bufchain *buf, const void *vdata, size_t len)
      * happen to get from its pipe, and whenever we have a complete
      * line, we pass it to plug_log.
      *
-     * Prerequisites: a plug to log to, and a bufchain stored
-     * somewhere to collect the data in.
+     * (We also do this when the buffer in psb fills up, to avoid just
+     * allocating more and more memory forever, and also to keep Event
+     * Log lines reasonably bounded in size.)
+     *
+     * Prerequisites: a plug to log to, and a ProxyStderrBuf stored
+     * somewhere to collect any not-yet-output partial line.
      */
 
-    while (pos < len && (nlpos = memchr(data+pos, '\n', len-pos)) != NULL) {
+    while (len > 0) {
         /*
-         * Found a newline in the current input buffer. Append it to
-         * the bufchain (which may contain a partial line from last
-         * time).
+         * Copy as much data into psb->buf as will fit.
          */
-        bufchain_add(buf, data + pos, nlpos - (data + pos));
+        assert(psb->size < lenof(psb->buf));
+        size_t to_consume = lenof(psb->buf) - psb->size;
+        if (to_consume > len)
+            to_consume = len;
+        memcpy(psb->buf + psb->size, data, to_consume);
+        data += to_consume;
+        len -= to_consume;
+        psb->size += to_consume;
 
         /*
-         * Collect the resulting line of data and pass it to plug_log.
+         * Output any full lines in psb->buf.
          */
-        size_t msglen = bufchain_size(buf);
-        assert(msglen < ~(size_t)0);
-        msg = snewn(msglen+1, char);
-        bufchain_fetch(buf, msg, msglen);
-        bufchain_consume(buf, msglen);
-        while (msglen > 0 && (msg[msglen-1] == '\n' || msg[msglen-1] == '\r'))
-            msglen--;
-        msg[msglen] = '\0';
-        fullmsg = dupprintf("proxy: %s", msg);
-        plug_log(plug, 2, NULL, 0, fullmsg, 0);
-        sfree(fullmsg);
-        sfree(msg);
+        size_t pos = 0;
+        while (pos < psb->size) {
+            char *nlpos = memchr(psb->buf + pos, '\n', psb->size - pos);
+            if (!nlpos)
+                break;
+
+            /*
+             * Found a newline in the buffer, so we can output a line.
+             */
+            size_t endpos = nlpos - psb->buf;
+            while (endpos > pos && (psb->buf[endpos-1] == '\n' ||
+                                    psb->buf[endpos-1] == '\r'))
+                endpos--;
+            char *msg = dupprintf(
+                "proxy: %.*s", (int)(endpos - pos), psb->buf + pos);
+            plug_log(plug, 2, NULL, 0, msg, 0);
+            sfree(msg);
+
+            pos = nlpos - psb->buf + 1;
+            assert(pos <= psb->size);
+        }
 
         /*
-         * Advance past the newline.
+         * If the buffer is completely full and we didn't output
+         * anything, then output the whole thing, flagging it as a
+         * truncated line.
+         */
+        if (pos == 0 && psb->size == lenof(psb->buf)) {
+            char *msg = dupprintf(
+                "proxy (partial line): %.*s", (int)psb->size, psb->buf);
+            plug_log(plug, 2, NULL, 0, msg, 0);
+            sfree(msg);
+
+            pos = psb->size = 0;
+        }
+
+        /*
+         * Now move any remaining data up to the front of the buffer.
+         */
+        size_t newsize = psb->size - pos;
+        if (newsize)
+            memmove(psb->buf, psb->buf + pos, newsize);
+        psb->size = newsize;
+
+        /*
+         * And loop round again if there's more data to be read from
+         * our input.
          */
-        pos += nlpos+1 - (data + pos);
     }
-
-    /*
-     * Now any remaining data is a partial line, which we save for
-     * next time.
-     */
-    bufchain_add(buf, data + pos, len - pos);
 }
diff --git a/network.h b/network.h
index 387c46f1..84287e72 100644
--- a/network.h
+++ b/network.h
@@ -290,7 +290,13 @@ void backend_socket_log(Seat *seat, LogContext *logctx,
                         int type, SockAddr *addr, int port,
                         const char *error_msg, int error_code, Conf *conf,
                         bool session_started);
+
+typedef struct ProxyStderrBuf {
+    char buf[8192];
+    size_t size;
+} ProxyStderrBuf;
+void psb_init(ProxyStderrBuf *psb);
 void log_proxy_stderr(
-    Plug *plug, bufchain *buf, const void *vdata, size_t len);
+    Plug *plug, ProxyStderrBuf *psb, const void *vdata, size_t len);
 
 #endif
diff --git a/unix/uxfdsock.c b/unix/uxfdsock.c
index 9ac3cdf8..54b29f6c 100644
--- a/unix/uxfdsock.c
+++ b/unix/uxfdsock.c
@@ -18,7 +18,7 @@ typedef struct FdSocket {
 
     bufchain pending_output_data;
     bufchain pending_input_data;
-    bufchain pending_input_error_data;
+    ProxyStderrBuf psb;
     enum { EOF_NO, EOF_PENDING, EOF_SENT } outgoingeof;
 
     int pending_error;
@@ -300,7 +300,7 @@ static void fdsocket_select_result_input_error(int fd, int event)
 
     retd = read(fd, buf, sizeof(buf));
     if (retd > 0) {
-        log_proxy_stderr(fds->plug, &fds->pending_input_error_data, buf, retd);
+        log_proxy_stderr(fds->plug, &fds->psb, buf, retd);
     } else {
         del234(fdsocket_by_inerrfd, fds);
         uxsel_del(fds->inerrfd);
@@ -337,7 +337,7 @@ Socket *make_fd_socket(int infd, int outfd, int inerrfd, Plug *plug)
 
     bufchain_init(&fds->pending_input_data);
     bufchain_init(&fds->pending_output_data);
-    bufchain_init(&fds->pending_input_error_data);
+    psb_init(&fds->psb);
 
     if (fds->outfd >= 0) {
         if (!fdsocket_by_outfd)
diff --git a/windows/winhsock.c b/windows/winhsock.c
index 4bebba75..5bbcfc2c 100644
--- a/windows/winhsock.c
+++ b/windows/winhsock.c
@@ -33,8 +33,8 @@ typedef struct HandleSocket {
     /* We buffer data here if we receive it from winhandl while frozen. */
     bufchain inputdata;
 
-    /* Data received from stderr_H, if we have one. */
-    bufchain stderrdata;
+    /* Handle logging proxy error messages from stderr_H, if we have one. */
+    ProxyStderrBuf psb;
 
     bool defer_close, deferred_close;   /* in case of re-entrance */
 
@@ -86,7 +86,7 @@ static size_t handle_stderr(
     HandleSocket *hs = (HandleSocket *)handle_get_privdata(h);
 
     if (!err && len > 0)
-        log_proxy_stderr(hs->plug, &hs->stderrdata, data, len);
+        log_proxy_stderr(hs->plug, &hs->psb, data, len);
 
     return 0;
 }
@@ -127,7 +127,6 @@ static void sk_handle_close(Socket *s)
     if (hs->recv_H != hs->send_H)
         CloseHandle(hs->recv_H);
     bufchain_clear(&hs->inputdata);
-    bufchain_clear(&hs->stderrdata);
 
     sfree(hs);
 }
@@ -332,7 +331,7 @@ Socket *make_handle_socket(HANDLE send_H, HANDLE recv_H, HANDLE stderr_H,
     hs->error = NULL;
     hs->frozen = UNFROZEN;
     bufchain_init(&hs->inputdata);
-    bufchain_init(&hs->stderrdata);
+    psb_init(&hs->psb);
 
     hs->recv_H = recv_H;
     hs->recv_h = handle_input_new(hs->recv_H, handle_gotdata, hs, flags);