diff --git a/composer.json b/composer.json
index 09263687d3d..68b7fe623be 100644
--- a/composer.json
+++ b/composer.json
@@ -45,7 +45,7 @@
         "phpunit/phpunit": "^8.5.5",
         "psalm/plugin-phpunit": "^0.10.0",
         "symfony/console": "^2.0.5|^3.0|^4.0|^5.0",
-        "vimeo/psalm": "^3.11"
+        "vimeo/psalm": "^3.11.4"
     },
     "suggest": {
         "symfony/console": "For helpful console commands such as SQL execution and import of files."
diff --git a/composer.lock b/composer.lock
index 3329a978cae..37114014b9a 100644
--- a/composer.lock
+++ b/composer.lock
@@ -4,7 +4,7 @@
         "Read more about it at https://getcomposer.org/doc/01-basic-usage.md#installing-dependencies",
         "This file is @generated automatically"
     ],
-    "content-hash": "9157c6d35dd39f5399592fd91126fa07",
+    "content-hash": "0372454a0ee2de4c2051cc13cbb23b72",
     "packages": [
         {
             "name": "doctrine/cache",
@@ -2995,16 +2995,16 @@
         },
         {
             "name": "vimeo/psalm",
-            "version": "3.11.2",
+            "version": "3.11.4",
             "source": {
                 "type": "git",
                 "url": "https://github.com/vimeo/psalm.git",
-                "reference": "d470903722cfcbc1cd04744c5491d3e6d13ec3d9"
+                "reference": "58e1d8e68e5098bf4fbfdfb420c38d563f882549"
             },
             "dist": {
                 "type": "zip",
-                "url": "https://api.github.com/repos/vimeo/psalm/zipball/d470903722cfcbc1cd04744c5491d3e6d13ec3d9",
-                "reference": "d470903722cfcbc1cd04744c5491d3e6d13ec3d9",
+                "url": "https://api.github.com/repos/vimeo/psalm/zipball/58e1d8e68e5098bf4fbfdfb420c38d563f882549",
+                "reference": "58e1d8e68e5098bf4fbfdfb420c38d563f882549",
                 "shasum": ""
             },
             "require": {
@@ -3089,7 +3089,7 @@
                 "inspection",
                 "php"
             ],
-            "time": "2020-04-13T12:47:11+00:00"
+            "time": "2020-05-11T13:39:25+00:00"
         },
         {
             "name": "webmozart/assert",
diff --git a/lib/Doctrine/DBAL/DriverManager.php b/lib/Doctrine/DBAL/DriverManager.php
index 95cb27c29d7..d3ed63a7f39 100644
--- a/lib/Doctrine/DBAL/DriverManager.php
+++ b/lib/Doctrine/DBAL/DriverManager.php
@@ -115,11 +115,15 @@ private function __construct()
      * <b>driverClass</b>:
      * The driver class to use.
      *
-     * @param mixed[]            $params       The parameters.
-     * @param Configuration|null $config       The configuration to use.
-     * @param EventManager|null  $eventManager The event manager to use.
+     * @param  array{wrapperClass?: class-string<T>} $params
+     * @param Configuration|null                    $config       The configuration to use.
+     * @param EventManager|null                     $eventManager The event manager to use.
      *
      * @throws DBALException
+     *
+     * @phpstan-param mixed[] $params
+     * @psalm-return ($params is array{wrapperClass:mixed} ? T : Connection)
+     * @template T of Connection
      */
     public static function getConnection(
         array $params,
diff --git a/phpstan.neon.dist b/phpstan.neon.dist
index 70544cbf7ec..40bc84910a1 100644
--- a/phpstan.neon.dist
+++ b/phpstan.neon.dist
@@ -83,3 +83,10 @@ parameters:
 
         # Needs Generics
         - '~Method Doctrine\\DBAL\\Schema\\SchemaDiff::getNewTablesSortedByDependencies\(\) should return array<Doctrine\\DBAL\\Schema\\Table> but returns array<object>.~'
+
+        # Caused by phpdoc annotations intended for Psalm
+        -
+            message: '~Unable to resolve the template type T in call to method static method Doctrine\\DBAL\\DriverManager::getConnection\(\)~'
+            paths:
+                - %currentWorkingDirectory%/lib/Doctrine/DBAL/Id/TableGenerator.php
+                - %currentWorkingDirectory%/lib/Doctrine/DBAL/Schema/SqliteSchemaManager.php