diff --git a/lib/Internal/Placeholder.php b/lib/Internal/Placeholder.php
index b84aa70..e0d2f0d 100644
--- a/lib/Internal/Placeholder.php
+++ b/lib/Internal/Placeholder.php
@@ -145,7 +145,10 @@ trait Placeholder
         }
 
         try {
-            /** @var mixed $result */
+            /**
+             * @var mixed $result
+             * @psalm-suppress PossiblyInvalidMethodCall https://github.com/vimeo/psalm/issues/3033
+             */
             $result = $onResolved(null, $this->result);
             $onResolved = null; // allow garbage collection of $onResolved, to catch any exceptions from destructors
 
diff --git a/lib/LazyPromise.php b/lib/LazyPromise.php
index f87a4d1..96be33f 100644
--- a/lib/LazyPromise.php
+++ b/lib/LazyPromise.php
@@ -12,7 +12,7 @@ final class LazyPromise implements Promise
     /** @var callable|null */
     private $promisor;
 
-    /** @var \Amp\Promise|null */
+    /** @var Promise|null */
     private $promise;
 
     /**
@@ -30,11 +30,15 @@ final class LazyPromise implements Promise
     public function onResolve(callable $onResolved)
     {
         if ($this->promise === null) {
+            \assert($this->promisor !== null);
+
             $provider = $this->promisor;
             $this->promisor = null;
             $this->promise = call($provider);
         }
 
+        \assert($this->promise !== null);
+
         $this->promise->onResolve($onResolved);
     }
 }
diff --git a/lib/Loop/Driver.php b/lib/Loop/Driver.php
index 57d6862..2d2ca19 100644
--- a/lib/Loop/Driver.php
+++ b/lib/Loop/Driver.php
@@ -182,6 +182,7 @@ abstract class Driver
      */
     public function defer(callable $callback, $data = null): string
     {
+        /** @psalm-var Watcher<null> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::DEFER;
         $watcher->id = $this->nextId++;
@@ -216,10 +217,12 @@ abstract class Driver
             throw new \Error("Delay must be greater than or equal to zero");
         }
 
+        /** @psalm-var Watcher<int> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::DELAY;
         $watcher->id = $this->nextId++;
         $watcher->callback = $callback;
+        /** @psalm-suppress InvalidPropertyAssignmentValue https://github.com/vimeo/psalm/issues/3035 */
         $watcher->value = $delay;
         $watcher->data = $data;
 
@@ -251,10 +254,12 @@ abstract class Driver
             throw new \Error("Interval must be greater than or equal to zero");
         }
 
+        /** @psalm-var Watcher<int> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::REPEAT;
         $watcher->id = $this->nextId++;
         $watcher->callback = $callback;
+        /** @psalm-suppress InvalidPropertyAssignmentValue https://github.com/vimeo/psalm/issues/3035 */
         $watcher->value = $interval;
         $watcher->data = $data;
 
@@ -285,10 +290,12 @@ abstract class Driver
      */
     public function onReadable($stream, callable $callback, $data = null): string
     {
+        /** @psalm-var Watcher<resource> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::READABLE;
         $watcher->id = $this->nextId++;
         $watcher->callback = $callback;
+        /** @psalm-suppress InvalidPropertyAssignmentValue https://github.com/vimeo/psalm/issues/3035 */
         $watcher->value = $stream;
         $watcher->data = $data;
 
@@ -319,10 +326,12 @@ abstract class Driver
      */
     public function onWritable($stream, callable $callback, $data = null): string
     {
+        /** @psalm-var Watcher<resource> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::WRITABLE;
         $watcher->id = $this->nextId++;
         $watcher->callback = $callback;
+        /** @psalm-suppress InvalidPropertyAssignmentValue https://github.com/vimeo/psalm/issues/3035 */
         $watcher->value = $stream;
         $watcher->data = $data;
 
@@ -354,10 +363,12 @@ abstract class Driver
      */
     public function onSignal(int $signo, callable $callback, $data = null): string
     {
+        /** @psalm-var Watcher<int> $watcher */
         $watcher = new Watcher;
         $watcher->type = Watcher::SIGNAL;
         $watcher->id = $this->nextId++;
         $watcher->callback = $callback;
+        /** @psalm-suppress InvalidPropertyAssignmentValue https://github.com/vimeo/psalm/issues/3035 */
         $watcher->value = $signo;
         $watcher->data = $data;
 
diff --git a/lib/Loop/EvDriver.php b/lib/Loop/EvDriver.php
index 0e1dc89..557294c 100644
--- a/lib/Loop/EvDriver.php
+++ b/lib/Loop/EvDriver.php
@@ -157,6 +157,8 @@ class EvDriver extends Driver
     {
         $active = self::$activeSignals;
 
+        \assert($active !== null);
+
         foreach ($active as $event) {
             $event->stop();
         }
@@ -230,10 +232,14 @@ class EvDriver extends Driver
             if (!isset($this->events[$id = $watcher->id])) {
                 switch ($watcher->type) {
                     case Watcher::READABLE:
+                        \assert(\is_resource($watcher->value));
+
                         $this->events[$id] = $this->handle->io($watcher->value, \Ev::READ, $this->ioCallback, $watcher);
                         break;
 
                     case Watcher::WRITABLE:
+                        \assert(\is_resource($watcher->value));
+
                         $this->events[$id] = $this->handle->io(
                             $watcher->value,
                             \Ev::WRITE,
@@ -244,6 +250,8 @@ class EvDriver extends Driver
 
                     case Watcher::DELAY:
                     case Watcher::REPEAT:
+                        \assert(\is_int($watcher->value));
+
                         $interval = $watcher->value / self::MILLISEC_PER_SEC;
                         $this->events[$id] = $this->handle->timer(
                             $interval,
@@ -254,6 +262,8 @@ class EvDriver extends Driver
                         break;
 
                     case Watcher::SIGNAL:
+                        \assert(\is_int($watcher->value));
+
                         $this->events[$id] = $this->handle->signal($watcher->value, $this->signalCallback, $watcher);
                         break;
 
@@ -267,6 +277,7 @@ class EvDriver extends Driver
             }
 
             if ($watcher->type === Watcher::SIGNAL) {
+                /** @psalm-suppress PropertyTypeCoercion */
                 $this->signals[$id] = $this->events[$id];
             }
         }
diff --git a/lib/Loop/EventDriver.php b/lib/Loop/EventDriver.php
index 5171725..54adfff 100644
--- a/lib/Loop/EventDriver.php
+++ b/lib/Loop/EventDriver.php
@@ -53,6 +53,8 @@ class EventDriver extends Driver
         }
 
         $this->ioCallback = function ($resource, $what, Watcher $watcher) {
+            \assert(\is_resource($watcher->value));
+
             try {
                 $result = ($watcher->callback)($watcher->id, $watcher->value, $watcher->data);
 
@@ -73,6 +75,8 @@ class EventDriver extends Driver
         };
 
         $this->timerCallback = function ($resource, $what, Watcher $watcher) {
+            \assert(\is_int($watcher->value));
+
             if ($watcher->type & Watcher::DELAY) {
                 $this->cancel($watcher->id);
             } else {
@@ -167,6 +171,8 @@ class EventDriver extends Driver
     {
         $active = self::$activeSignals;
 
+        \assert($active !== null);
+
         foreach ($active as $event) {
             $event->del();
         }
@@ -244,6 +250,8 @@ class EventDriver extends Driver
             if (!isset($this->events[$id = $watcher->id])) {
                 switch ($watcher->type) {
                     case Watcher::READABLE:
+                        \assert(\is_resource($watcher->value));
+
                         $this->events[$id] = new \Event(
                             $this->handle,
                             $watcher->value,
@@ -254,6 +262,8 @@ class EventDriver extends Driver
                         break;
 
                     case Watcher::WRITABLE:
+                        \assert(\is_resource($watcher->value));
+
                         $this->events[$id] = new \Event(
                             $this->handle,
                             $watcher->value,
@@ -265,6 +275,8 @@ class EventDriver extends Driver
 
                     case Watcher::DELAY:
                     case Watcher::REPEAT:
+                        \assert(\is_int($watcher->value));
+
                         $this->events[$id] = new \Event(
                             $this->handle,
                             -1,
@@ -275,6 +287,8 @@ class EventDriver extends Driver
                         break;
 
                     case Watcher::SIGNAL:
+                        \assert(\is_int($watcher->value));
+
                         $this->events[$id] = new \Event(
                             $this->handle,
                             $watcher->value,
@@ -294,6 +308,8 @@ class EventDriver extends Driver
             switch ($watcher->type) {
                 case Watcher::DELAY:
                 case Watcher::REPEAT:
+                    \assert(\is_int($watcher->value));
+
                     $interval = $watcher->value - ($now - $this->now());
                     $this->events[$id]->add($interval > 0 ? $interval / self::MILLISEC_PER_SEC : 0);
                     break;
diff --git a/lib/Loop/Internal/TimerQueue.php b/lib/Loop/Internal/TimerQueue.php
index cabc455..6ec63d0 100644
--- a/lib/Loop/Internal/TimerQueue.php
+++ b/lib/Loop/Internal/TimerQueue.php
@@ -21,6 +21,8 @@ final class TimerQueue
      * @param Watcher $watcher
      * @param int     $expiration
      *
+     * @psalm-param Watcher<int> $watcher
+     *
      * @return void
      */
     public function insert(Watcher $watcher, int $expiration)
@@ -32,6 +34,8 @@ final class TimerQueue
         $this->pointers[$watcher->id] = $node;
 
         while ($node !== 0 && $entry->expiration < $this->data[$parent = ($node - 1) >> 1]->expiration) {
+            \assert(isset($parent)); // see https://github.com/vimeo/psalm/issues/3034
+
             $temp = $this->data[$parent];
             $this->data[$node] = $temp;
             $this->pointers[$temp->watcher->id] = $node;
@@ -48,6 +52,8 @@ final class TimerQueue
      *
      * @param Watcher $watcher
      *
+     * @psalm-param Watcher<int> $watcher
+     *
      * @return void
      */
     public function remove(Watcher $watcher)
@@ -68,6 +74,8 @@ final class TimerQueue
      * @param int $now Current loop time.
      *
      * @return Watcher|null Expired watcher at the top of the heap or null if the watcher has not expired.
+     *
+     * @psalm-return Watcher<int>|null
      */
     public function extract(int $now)
     {
diff --git a/lib/Loop/NativeDriver.php b/lib/Loop/NativeDriver.php
index 5be332b..c066019 100644
--- a/lib/Loop/NativeDriver.php
+++ b/lib/Loop/NativeDriver.php
@@ -217,6 +217,8 @@ class NativeDriver extends Driver
                 }
             }
 
+            \assert(\is_array($write)); // See https://github.com/vimeo/psalm/issues/3036
+
             foreach ($write as $stream) {
                 $streamId = (int) $stream;
                 if (!isset($this->writeWatchers[$streamId])) {
diff --git a/lib/Loop/Watcher.php b/lib/Loop/Watcher.php
index 7a9002b..4bace62 100644
--- a/lib/Loop/Watcher.php
+++ b/lib/Loop/Watcher.php
@@ -4,6 +4,9 @@ namespace Amp\Loop;
 
 use Amp\Struct;
 
+/**
+ * @template TValue as (int|resource|null)
+ */
 class Watcher
 {
     use Struct;
@@ -42,7 +45,8 @@ class Watcher
     /**
      * Watcher-dependent value storage. Stream for IO watchers, signal number for signal watchers, interval for timers.
      *
-     * @var resource|int
+     * @var resource|int|null
+     * @psalm-var TValue
      */
     public $value;
 }
diff --git a/psalm.xml b/psalm.xml
index d6aa085..97b60ea 100644
--- a/psalm.xml
+++ b/psalm.xml
@@ -1,7 +1,7 @@
 <?xml version="1.0"?>
 <psalm
         totallyTyped="false"
-        errorLevel="4"
+        errorLevel="3"
         phpVersion="7.0"
         resolveFromConfigFile="true"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"