diff --git a/packages/pg-cursor/index.js b/packages/pg-cursor/index.js
index 5d566882b..5284e46bd 100644
--- a/packages/pg-cursor/index.js
+++ b/packages/pg-cursor/index.js
@@ -27,7 +27,10 @@ class Cursor extends EventEmitter {
   }
 
   _ifNoData() {
-    if (this.state !== 'done' && this.state !== 'error') {
+    // Only start a queued read when the portal is first ready. An in-flight
+    // execute (state === 'busy') must not be interrupted, and closed/failed
+    // cursors must stay closed.
+    if (this.state === 'submitted' || this.state === 'initialized') {
       this.state = 'idle'
       this._shiftQueue()
     }
@@ -108,7 +111,9 @@ class Cursor extends EventEmitter {
 
   handleRowDescription(msg) {
     this._result.addFields(msg.fields)
-    if (this.state !== 'done' && this.state !== 'error') {
+    // If read() already sent Execute (state === 'busy'), keep that in-flight
+    // callback. Resetting to idle here would start a queued read and overwrite _cb.
+    if (this.state === 'submitted' || this.state === 'initialized') {
       this.state = 'idle'
       this._shiftQueue()
     }
@@ -124,23 +129,40 @@ class Cursor extends EventEmitter {
     if (this.state !== 'done') {
       this.state = 'idle'
     }
-    setImmediate(() => {
-      const cb = this._cb
-      // remove callback before calling it
-      // because likely a new one will be added
-      // within the call to this callback
-      this._cb = null
-      if (cb) {
-        this._result.rows = this._rows
-        cb(null, this._rows, this._result)
-      }
-      this._rows = []
-    })
+    const cb = this._cb
+    const rows = this._rows
+    // Drop the callback synchronously so a later ReadyForQuery cannot
+    // deliver the same batch twice after CommandComplete already settled it.
+    this._cb = null
+    this._rows = []
+    if (this.state === 'idle') {
+      this._shiftQueue()
+    }
+    if (cb) {
+      setImmediate(() => {
+        this._result.rows = rows
+        cb(null, rows, this._result)
+      })
+    }
+  }
+
+  _fulfillQueue(err, rows) {
+    const queue = this._queue.splice(0, this._queue.length)
+    for (let i = 0; i < queue.length; i++) {
+      const queuedCallback = queue[i][1]
+      setImmediate(() => queuedCallback.call(this, err, rows))
+    }
   }
 
   handleCommandComplete(msg) {
     this._result.addCommandComplete(msg)
     this._closePortal()
+    // CommandComplete means the portal is exhausted. Settle the in-flight
+    // read with whatever rows remain (possibly fewer than requested, or none)
+    // instead of waiting for ReadyForQuery, which the client may never
+    // dispatch to this cursor.
+    this._sendRows()
+    this._fulfillQueue(null, [])
   }
 
   handlePortalSuspended() {
@@ -150,6 +172,7 @@ class Cursor extends EventEmitter {
   handleReadyForQuery() {
     this._sendRows()
     this.state = 'done'
+    this._fulfillQueue(null, [])
     this.emit('end', this._result)
   }
 
diff --git a/packages/pg-cursor/test/read-exhaustion.js b/packages/pg-cursor/test/read-exhaustion.js
new file mode 100644
index 000000000..d4ca6e018
--- /dev/null
+++ b/packages/pg-cursor/test/read-exhaustion.js
@@ -0,0 +1,161 @@
+const assert = require('assert')
+const EventEmitter = require('events')
+const Cursor = require('../')
+const pg = require('pg')
+
+class TestConnection extends EventEmitter {
+  constructor() {
+    super()
+    this.calls = {
+      close: 0,
+      execute: 0,
+      sync: 0,
+    }
+  }
+
+  parse() {}
+  bind() {}
+  describe() {}
+  flush() {}
+
+  execute() {
+    this.calls.execute++
+  }
+
+  close() {
+    this.calls.close++
+  }
+
+  sync() {
+    this.calls.sync++
+  }
+}
+
+const INT4 = { name: 'num', dataTypeID: 23 }
+
+const pushIntRows = (cursor, values) => {
+  for (const value of values) {
+    cursor.handleDataRow({ fields: [String(value)] })
+  }
+}
+
+const settleOrTimeout = (promise, ms = 150) =>
+  Promise.race([
+    promise.then((value) => ({ value })),
+    new Promise((resolve) => setTimeout(() => resolve({ timeout: true }), ms)),
+  ])
+
+describe('read() when rowCount exceeds remaining rows (#2949)', function () {
+  it('settles as soon as the portal is exhausted', async function () {
+    const cursor = new Cursor('SELECT num FROM generate_series(1, 2) num')
+    const connection = new TestConnection()
+    cursor.submit(connection)
+
+    const read = cursor.read(1000)
+    cursor.handleRowDescription({ fields: [INT4] })
+    pushIntRows(cursor, [1, 2])
+    cursor.handleCommandComplete({ text: 'SELECT 2' })
+
+    const outcome = await settleOrTimeout(read)
+    assert.ok(!outcome.timeout, 'read() hung after CommandComplete when rowCount exceeded remaining rows')
+    assert.deepStrictEqual(outcome.value, [{ num: 1 }, { num: 2 }])
+    assert.strictEqual(cursor.state, 'done')
+    assert.deepStrictEqual(connection.calls, { close: 1, execute: 1, sync: 1 })
+  })
+
+  it('returns a shorter batch when only some rows remain', async function () {
+    const cursor = new Cursor('SELECT num FROM generate_series(1, 5) num')
+    const connection = new TestConnection()
+    cursor.submit(connection)
+    cursor.handleRowDescription({ fields: [INT4] })
+
+    const first = cursor.read(3)
+    pushIntRows(cursor, [1, 2, 3])
+    cursor.handlePortalSuspended()
+    assert.deepStrictEqual(await first, [{ num: 1 }, { num: 2 }, { num: 3 }])
+
+    const remaining = cursor.read(1000)
+    pushIntRows(cursor, [4, 5])
+    cursor.handleCommandComplete({ text: 'SELECT 5' })
+
+    const outcome = await settleOrTimeout(remaining)
+    assert.ok(!outcome.timeout, 'read() hung when fetching more rows than remained')
+    assert.deepStrictEqual(outcome.value, [{ num: 4 }, { num: 5 }])
+  })
+
+  it('settles queued reads with leftover or empty rows once the portal is exhausted', async function () {
+    const cursor = new Cursor('SELECT num FROM generate_series(1, 2) num')
+    const connection = new TestConnection()
+    cursor.submit(connection)
+
+    const first = cursor.read(1000)
+    const queued = cursor.read(1000)
+    cursor.handleRowDescription({ fields: [INT4] })
+    pushIntRows(cursor, [1, 2])
+    cursor.handleCommandComplete({ text: 'SELECT 2' })
+
+    const firstOutcome = await settleOrTimeout(first)
+    const queuedOutcome = await settleOrTimeout(queued)
+    assert.ok(!firstOutcome.timeout, 'in-flight read hung after the portal was exhausted')
+    assert.ok(!queuedOutcome.timeout, 'queued read hung after the portal was exhausted')
+    assert.deepStrictEqual(firstOutcome.value, [{ num: 1 }, { num: 2 }])
+    assert.deepStrictEqual(queuedOutcome.value, [])
+  })
+
+  it('keeps an in-flight oversized read when row description arrives late', async function () {
+    const cursor = new Cursor('SELECT num FROM generate_series(1, 2) num')
+    const connection = new TestConnection()
+    cursor.submit(connection)
+
+    const first = cursor.read(1000)
+    const queued = cursor.read(5)
+    cursor.handleRowDescription({ fields: [INT4] })
+    pushIntRows(cursor, [1, 2])
+    cursor.handleCommandComplete({ text: 'SELECT 2' })
+
+    const firstOutcome = await settleOrTimeout(first)
+    const queuedOutcome = await settleOrTimeout(queued)
+    assert.ok(!firstOutcome.timeout, 'in-flight read was overwritten when row description arrived')
+    assert.ok(!queuedOutcome.timeout, 'queued read hung after a late row description')
+    assert.deepStrictEqual(firstOutcome.value, [{ num: 1 }, { num: 2 }])
+    assert.deepStrictEqual(queuedOutcome.value, [])
+    assert.strictEqual(connection.calls.execute, 1)
+  })
+})
+
+describe('read() against PostgreSQL when rowCount exceeds remaining rows (#2949)', function () {
+  beforeEach(function (done) {
+    const client = (this.client = new pg.Client())
+    client.connect(done)
+  })
+
+  afterEach(function () {
+    this.client.end()
+  })
+
+  it('returns all 100 rows when asked for 1000', function (done) {
+    const cursor = this.client.query(new Cursor('SELECT generate_series as num FROM generate_series(1, 100)'))
+    cursor.read(1000, function (err, rows) {
+      assert.ifError(err)
+      assert.strictEqual(rows.length, 100)
+      assert.strictEqual(rows[0].num, 1)
+      assert.strictEqual(rows[99].num, 100)
+      cursor.read(1000, function (err, empty) {
+        assert.ifError(err)
+        assert.strictEqual(empty.length, 0)
+        done()
+      })
+    })
+  })
+
+  it('returns the leftover rows after a partial page', async function () {
+    const cursor = this.client.query(new Cursor('SELECT generate_series as num FROM generate_series(1, 100)'))
+    const first = await cursor.read(40)
+    assert.strictEqual(first.length, 40)
+    const remaining = await cursor.read(1000)
+    assert.strictEqual(remaining.length, 60)
+    assert.strictEqual(remaining[0].num, 41)
+    assert.strictEqual(remaining[59].num, 100)
+    assert.deepStrictEqual(await cursor.read(1000), [])
+  })
+})