diff --git a/tests/unit/data/postgres.sql b/tests/unit/data/postgres.sql
index 071d25133f..c5656f2ad0 100644
--- a/tests/unit/data/postgres.sql
+++ b/tests/unit/data/postgres.sql
@@ -4,6 +4,7 @@
  * and create an account 'postgres/postgres' which owns this test database.
  */
 
+DROP TABLE IF EXISTS "composite_fk" CASCADE;
 DROP TABLE IF EXISTS "order_item" CASCADE;
 DROP TABLE IF EXISTS "item" CASCADE;
 DROP TABLE IF EXISTS "order_item_with_null_fk" CASCADE;
@@ -78,6 +79,14 @@ CREATE TABLE "order_item_with_null_fk" (
   subtotal decimal(10,0) NOT NULL
 );
 
+CREATE TABLE "composite_fk" (
+  id integer NOT NULL,
+  order_id integer NOT NULL,
+  item_id integer NOT NULL,
+  PRIMARY KEY (id),
+  CONSTRAINT FK_composite_fk_order_item FOREIGN KEY (order_id, item_id) REFERENCES "order_item" (order_id, item_id) ON DELETE CASCADE
+);
+
 CREATE TABLE "null_values" (
   id INT NOT NULL,
   var1 INT NULL,
@@ -101,7 +110,7 @@ CREATE TABLE "type" (
   bool_col smallint NOT NULL,
   bool_col2 smallint DEFAULT '1',
   ts_default TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
-  bit_col BIT NOT NULL DEFAULT B'10000010'
+  bit_col BIT(8) NOT NULL DEFAULT B'10000010'
 );
 
 INSERT INTO "profile" (description) VALUES ('profile customer 1');
diff --git a/tests/unit/framework/db/BatchQueryResultTest.php b/tests/unit/framework/db/BatchQueryResultTest.php
index 0097415465..b5b10b3f76 100644
--- a/tests/unit/framework/db/BatchQueryResultTest.php
+++ b/tests/unit/framework/db/BatchQueryResultTest.php
@@ -14,8 +14,8 @@ use yii\db\BatchQueryResult;
 use yiiunit\data\ar\Customer;
 
 /**
- * @author Qiang Xue <qiang.xue@gmail.com>
- * @since 2.0
+ * @group db
+ * @group mysql
  */
 class BatchQueryResultTest extends DatabaseTestCase
 {
diff --git a/tests/unit/framework/db/CommandTest.php b/tests/unit/framework/db/CommandTest.php
index 0bb51bf33e..d6a587b0f1 100644
--- a/tests/unit/framework/db/CommandTest.php
+++ b/tests/unit/framework/db/CommandTest.php
@@ -159,7 +159,7 @@ class CommandTest extends DatabaseTestCase
         $sql = 'INSERT INTO type (int_col, char_col, float_col, blob_col, numeric_col, bool_col) VALUES (:int_col, :char_col, :float_col, :blob_col, :numeric_col, :bool_col)';
         $command = $db->createCommand($sql);
         $intCol = 123;
-        $charCol = 'abc';
+        $charCol = str_repeat('abc', 33) . 'x'; // a 100 char string
         $floatCol = 1.23;
         $blobCol = "\x10\x11\x12";
         $numericCol = '1.23';
@@ -172,13 +172,21 @@ class CommandTest extends DatabaseTestCase
         $command->bindParam(':bool_col', $boolCol);
         $this->assertEquals(1, $command->execute());
 
-        $sql = 'SELECT * FROM type';
-        $row = $db->createCommand($sql)->queryOne();
+        $command = $db->createCommand('SELECT int_col, char_col, float_col, blob_col, numeric_col, bool_col FROM type');
+//        $command->prepare();
+//        $command->pdoStatement->bindColumn('blob_col', $bc, \PDO::PARAM_LOB);
+        $row = $command->queryOne();
         $this->assertEquals($intCol, $row['int_col']);
         $this->assertEquals($charCol, $row['char_col']);
         $this->assertEquals($floatCol, $row['float_col']);
-        $this->assertEquals($blobCol, $row['blob_col']);
+        if ($this->driverName === 'mysql' || $this->driverName === 'sqlite') {
+            $this->assertEquals($blobCol, $row['blob_col']);
+        } else {
+            $this->assertTrue(is_resource($row['blob_col']));
+            $this->assertEquals($blobCol, stream_get_contents($row['blob_col']));
+        }
         $this->assertEquals($numericCol, $row['numeric_col']);
+        $this->assertEquals($boolCol, $row['bool_col']);
 
         // bindValue
         $sql = 'INSERT INTO customer(email, name, address) VALUES (:email, \'user5\', \'address5\')';
diff --git a/tests/unit/framework/db/SchemaTest.php b/tests/unit/framework/db/SchemaTest.php
index e826bba591..b9f783ebe5 100644
--- a/tests/unit/framework/db/SchemaTest.php
+++ b/tests/unit/framework/db/SchemaTest.php
@@ -87,7 +87,7 @@ class SchemaTest extends DatabaseTestCase
         $schema = $this->getConnection()->schema;
 
         foreach ($values as $value) {
-            $this->assertEquals($value[1], $schema->getPdoType($value[0]));
+            $this->assertEquals($value[1], $schema->getPdoType($value[0]), 'type for value ' . print_r($value[0], true) . ' does not match.');
         }
         fclose($fp);
     }
diff --git a/tests/unit/framework/db/pgsql/PostgreSQLCommandTest.php b/tests/unit/framework/db/pgsql/PostgreSQLCommandTest.php
index 0bbb8d429c..b810a0a770 100644
--- a/tests/unit/framework/db/pgsql/PostgreSQLCommandTest.php
+++ b/tests/unit/framework/db/pgsql/PostgreSQLCommandTest.php
@@ -3,6 +3,10 @@ namespace yii\tests\unit\framework\db\pgsql;
 
 use yiiunit\framework\db\CommandTest;
 
+/**
+ * @group db
+ * @group pgsql
+ */
 class PostgreSQLCommandTest extends CommandTest
 {
     public $driverName = 'pgsql';
@@ -15,9 +19,4 @@ class PostgreSQLCommandTest extends CommandTest
         $command = $db->createCommand($sql);
         $this->assertEquals('SELECT "id", "t"."name" FROM "customer" t', $command->sql);
     }
-
-    public function testBindParamValue()
-    {
-        $this->markTestIncomplete('TODO: impement it');
-    }
-} 
\ No newline at end of file
+}
\ No newline at end of file
diff --git a/tests/unit/framework/db/pgsql/PostgreSQLSchemaTest.php b/tests/unit/framework/db/pgsql/PostgreSQLSchemaTest.php
index df94f5f5a3..a93027aad2 100644
--- a/tests/unit/framework/db/pgsql/PostgreSQLSchemaTest.php
+++ b/tests/unit/framework/db/pgsql/PostgreSQLSchemaTest.php
@@ -53,8 +53,31 @@ class PostgreSQLSchemaTest extends SchemaTest
         $columns['bool_col2']['scale'] = 0;
         $columns['ts_default']['defaultValue'] = new Expression('now()');
         $columns['bit_col']['dbType'] = 'bit';
-        $columns['bit_col']['size'] = 1; // TODO should be 8???
+        $columns['bit_col']['size'] = 8;
         $columns['bit_col']['precision'] = null;
         return $columns;
     }
+
+    public function testGetPDOType()
+    {
+        $values = [
+            [null, \PDO::PARAM_NULL],
+            ['', \PDO::PARAM_STR],
+            ['hello', \PDO::PARAM_STR],
+            [0, \PDO::PARAM_INT],
+            [1, \PDO::PARAM_INT],
+            [1337, \PDO::PARAM_INT],
+            [true, \PDO::PARAM_INT],
+            [false, \PDO::PARAM_INT],
+            [$fp = fopen(__FILE__, 'rb'), \PDO::PARAM_LOB],
+        ];
+
+        /* @var $schema Schema */
+        $schema = $this->getConnection()->schema;
+
+        foreach ($values as $value) {
+            $this->assertEquals($value[1], $schema->getPdoType($value[0]));
+        }
+        fclose($fp);
+    }
 }
diff --git a/tests/unit/framework/db/sqlite/SqliteQueryBuilderTest.php b/tests/unit/framework/db/sqlite/SqliteQueryBuilderTest.php
index ef7387ce98..3d5a861833 100644
--- a/tests/unit/framework/db/sqlite/SqliteQueryBuilderTest.php
+++ b/tests/unit/framework/db/sqlite/SqliteQueryBuilderTest.php
@@ -84,6 +84,9 @@ class SqliteQueryBuilderTest extends QueryBuilderTest
 
     public function testBatchInsert()
     {
+        if (version_compare(\SQLite3::version()['versionString'], '3.7.11', '>=')) {
+            $this->markTestSkipped('This test is only relevant for SQLite < 3.7.11');
+        }
         $sql = $this->getQueryBuilder()->batchInsert('{{customer}} t', ['t.id', 't.name'], [[1, 'a'], [2, 'b']]);
         $this->assertEquals("INSERT INTO {{customer}} t (`t`.`id`, `t`.`name`) SELECT 1, 'a' UNION SELECT 2, 'b'", $sql);
     }