diff --git a/packages/pg-cursor/index.js b/packages/pg-cursor/index.js
index 5d566882b..cdf4aa3c7 100644
--- a/packages/pg-cursor/index.js
+++ b/packages/pg-cursor/index.js
@@ -27,7 +27,7 @@ class Cursor extends EventEmitter {
   }
 
   _ifNoData() {
-    if (this.state !== 'done' && this.state !== 'error') {
+    if (this.state !== 'done' && this.state !== 'error' && this.state !== 'busy') {
       this.state = 'idle'
       this._shiftQueue()
     }
@@ -108,7 +108,7 @@ class Cursor extends EventEmitter {
 
   handleRowDescription(msg) {
     this._result.addFields(msg.fields)
-    if (this.state !== 'done' && this.state !== 'error') {
+    if (this.state !== 'done' && this.state !== 'error' && this.state !== 'busy') {
       this.state = 'idle'
       this._shiftQueue()
     }
@@ -135,6 +135,12 @@ class Cursor extends EventEmitter {
         cb(null, this._rows, this._result)
       }
       this._rows = []
+      // the active read just settled; start any read queued behind it.
+      // the callback above may have started a new read itself, so only
+      // shift when the cursor is idle again.
+      if (this.state === 'idle') {
+        this._shiftQueue()
+      }
     })
   }
 
diff --git a/packages/pg-cursor/test/concurrent-reads.js b/packages/pg-cursor/test/concurrent-reads.js
new file mode 100644
index 000000000..69d40ad61
--- /dev/null
+++ b/packages/pg-cursor/test/concurrent-reads.js
@@ -0,0 +1,33 @@
+const assert = require('assert')
+const Cursor = require('../')
+const pg = require('pg')
+
+const text = 'SELECT generate_series AS num FROM generate_series(1, 5)'
+
+describe('concurrent reads', function () {
+  beforeEach(function (done) {
+    const client = (this.client = new pg.Client())
+    client.connect(done)
+  })
+
+  afterEach(function () {
+    this.client.end()
+  })
+
+  it('settles every read when two reads overlap', async function () {
+    const cursor = this.client.query(new Cursor(text))
+    const first = cursor.read(1)
+    const second = cursor.read(1)
+    const [rowsA, rowsB] = await Promise.all([first, second])
+    assert.strictEqual(rowsA.length, 1)
+    assert.strictEqual(rowsB.length, 1)
+    assert.strictEqual(rowsA[0].num, 1)
+    assert.strictEqual(rowsB[0].num, 2)
+    const rest = await cursor.read(10)
+    assert.deepStrictEqual(
+      rest.map((row) => row.num),
+      [3, 4, 5]
+    )
+    await cursor.close()
+  })
+})