diff --git a/lib/internal/fs/streams.js b/lib/internal/fs/streams.js
index f527b1de4b84a4..92bd9a4c15fa23 100644
--- a/lib/internal/fs/streams.js
+++ b/lib/internal/fs/streams.js
@@ -21,9 +21,18 @@ const util = require('util');
 const kMinPoolSpace = 128;
 
 let pool;
+// It can happen that we expect to read a large chunk of data, and reserve
+// a large chunk of the pool accordingly, but the read() call only filled
+// a portion of it. If a concurrently executing read() then uses the same pool,
+// the "reserved" portion cannot be used, so we allow it to be re-used as a
+// new pool later.
+const poolFragments = [];
 
 function allocNewPool(poolSize) {
-  pool = Buffer.allocUnsafe(poolSize);
+  if (poolFragments.length > 0)
+    pool = poolFragments.pop();
+  else
+    pool = Buffer.allocUnsafe(poolSize);
   pool.used = 0;
 }
 
@@ -171,6 +180,14 @@ ReadStream.prototype._read = function(n) {
       this.emit('error', er);
     } else {
       let b = null;
+      // Now that we know how much data we have actually read, re-wind the
+      // 'used' field if we can, and otherwise allow the remainder of our
+      // reservation to be used as a new pool later.
+      if (start + toRead === thisPool.used && thisPool === pool)
+        thisPool.used += bytesRead - toRead;
+      else if (toRead - bytesRead > kMinPoolSpace)
+        poolFragments.push(thisPool.slice(start + bytesRead, start + toRead));
+
       if (bytesRead > 0) {
         this.bytesRead += bytesRead;
         b = thisPool.slice(start, start + bytesRead);
diff --git a/test/parallel/test-fs-read-stream-concurrent-reads.js b/test/parallel/test-fs-read-stream-concurrent-reads.js
new file mode 100644
index 00000000000000..32a6cd62363f05
--- /dev/null
+++ b/test/parallel/test-fs-read-stream-concurrent-reads.js
@@ -0,0 +1,47 @@
+'use strict';
+const common = require('../common');
+const fixtures = require('../common/fixtures');
+const assert = require('assert');
+const fs = require('fs');
+
+// Test that concurrent file read streams don’t interfere with each other’s
+// contents, and that the chunks generated by the reads only retain a
+// 'reasonable' amount of memory.
+
+// Refs: https://github.com/nodejs/node/issues/21967
+
+const filename = fixtures.path('loop.js');  // Some small non-homogeneous file.
+const content = fs.readFileSync(filename);
+
+const N = 1000;
+let started = 0;
+let done = 0;
+
+const arrayBuffers = new Set();
+
+function startRead() {
+  ++started;
+  const chunks = [];
+  fs.createReadStream(filename)
+    .on('data', (chunk) => {
+      chunks.push(chunk);
+      arrayBuffers.add(chunk.buffer);
+      if (started < N)
+        startRead();
+    })
+    .on('end', common.mustCall(() => {
+      assert.deepStrictEqual(Buffer.concat(chunks), content);
+      if (++done === N) {
+        const retainedMemory =
+          [...arrayBuffers].map((ab) => ab.byteLength).reduce((a, b) => a + b);
+        assert(retainedMemory / (N * content.length) <= 3,
+               `Retaining ${retainedMemory} bytes in ABs for ${N} ` +
+               `chunks of size ${content.length}`);
+      }
+    }));
+}
+
+// Don’t start the reads all at once – that way we would have to allocate
+// a large amount of memory upfront.
+for (let i = 0; i < 4; ++i)
+  startRead();