diff --git a/src/connection.js b/src/connection.js
index 97cc97e1..d98dded1 100644
--- a/src/connection.js
+++ b/src/connection.js
@@ -884,6 +884,7 @@ function Connection(options, queues = {}, { onopen = noop, onend = noop, onclose
   function CopyDone() {
     stream && stream.push(null)
     stream = null
+    socket.isPaused() && socket.resume()
   }
 
   function NoticeResponse(x) {
diff --git a/tests/index.js b/tests/index.js
index bf81b036..0c175911 100644
--- a/tests/index.js
+++ b/tests/index.js
@@ -4,6 +4,7 @@ import { t, nt, ot } from './test.js' // eslint-disable-line
 import net from 'net'
 import fs from 'fs'
 import crypto from 'crypto'
+import stream from 'stream'
 
 import postgres from '../src/index.js'
 const delay = ms => new Promise(r => setTimeout(r, ms))
@@ -1914,6 +1915,46 @@ t('Copy read', async() => {
   ]
 })
 
+t('Copy read with back-pressure', async() => {
+  await sql`create table test (x int)`
+
+  // Make sure there are enough rows in the table to fill the buffer
+  // so that `CopyDone` message is handled while the socket is paused
+  const bufferSize = Math.ceil((stream.getDefaultHighWaterMark || (() => 16384))() / 6)
+  await sql`insert into test select * from generate_series(10000,${9999 + bufferSize})`
+
+  let result = 0
+  const readable = await sql`copy test to stdout`.readable()
+  readable.on('data', () => result++)
+
+  // Pause the stream so that the entire buffer fills up
+  readable.pause()
+
+  await Promise.all([
+    // Wait until the stream has been consumed
+    new Promise(r => readable.on('end', r)),
+    (async() => {
+      // Wait until the entire buffer fills up,
+      await new Promise(r => readable.on('readable', () => {
+        if (readable.readableBuffer.length === bufferSize)
+          r()
+      }))
+      // Switch the stream back to flowing mode (allowing it to be consumed)
+      readable.removeAllListeners('readable')
+    })()
+  ])
+
+  // This is the actual test, the copy stream is done
+  // we should be able to run a new query
+  await sql`SELECT 1`
+
+  return [
+    result,
+    bufferSize,
+    await sql`drop table test`
+  ]
+})
+
 t('Copy write', { timeout: 2 }, async() => {
   await sql`create table test (x int)`
   const writable = await sql`copy test from stdin`.writable()