diff --git a/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/h2/H2Tests.kt b/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/h2/H2Tests.kt
index 766e7ab017..35e868a4c0 100644
--- a/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/h2/H2Tests.kt
+++ b/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/h2/H2Tests.kt
@@ -1,8 +1,11 @@
 package org.jetbrains.exposed.sql.tests.h2
 
+import org.jetbrains.exposed.dao.id.IntIdTable
 import org.jetbrains.exposed.sql.*
 import org.jetbrains.exposed.sql.tests.DatabaseTestsBase
 import org.jetbrains.exposed.sql.tests.TestDB
+import org.jetbrains.exposed.sql.tests.currentDialectTest
+import org.jetbrains.exposed.sql.tests.inProperCase
 import org.jetbrains.exposed.sql.tests.shared.assertEquals
 import org.jetbrains.exposed.sql.transactions.TransactionManager
 import org.jetbrains.exposed.sql.transactions.transactionManager
@@ -93,6 +96,28 @@ class H2Tests : DatabaseTestsBase() {
         }
     }
 
+    @Test
+    fun addAutoPrimaryKey() {
+        val tableName = "Foo"
+        val initialTable = object : Table(tableName) {
+            val bar = text("bar")
+        }
+        val t = IntIdTable(tableName)
+
+        withDb(listOf(TestDB.H2, TestDB.H2_MYSQL)) {
+            try {
+                SchemaUtils.createMissingTablesAndColumns(initialTable)
+                assertEquals("ALTER TABLE ${tableName.inProperCase()} ADD ${"id".inProperCase()} ${t.id.columnType.sqlType()}", t.id.ddl.first())
+                assertEquals("ALTER TABLE ${tableName.inProperCase()} ADD CONSTRAINT pk_$tableName PRIMARY KEY (${"id".inProperCase()})", t.id.ddl[1])
+                assertEquals(1, currentDialectTest.tableColumns(t)[t]!!.size)
+                SchemaUtils.createMissingTablesAndColumns(t)
+                assertEquals(2, currentDialectTest.tableColumns(t)[t]!!.size)
+            } finally {
+                SchemaUtils.drop(t)
+            }
+        }
+    }
+
     class WrappedTransactionManager(val transactionManager: TransactionManager) :
         TransactionManager by transactionManager
 
diff --git a/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/shared/ddl/CreateMissingTablesAndColumnsTests.kt b/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/shared/ddl/CreateMissingTablesAndColumnsTests.kt
index 3536402b06..de07bb558f 100644
--- a/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/shared/ddl/CreateMissingTablesAndColumnsTests.kt
+++ b/exposed-tests/src/test/kotlin/org/jetbrains/exposed/sql/tests/shared/ddl/CreateMissingTablesAndColumnsTests.kt
@@ -248,27 +248,6 @@ class CreateMissingTablesAndColumnsTests : DatabaseTestsBase() {
         }
         val t = IntIdTable(tableName)
 
-        withDb(TestDB.H2) {
-            SchemaUtils.createMissingTablesAndColumns(initialTable)
-            assertEquals("ALTER TABLE ${tableName.inProperCase()} ADD ${"id".inProperCase()} ${t.id.columnType.sqlType()}", t.id.ddl.first())
-            assertEquals("ALTER TABLE ${tableName.inProperCase()} ADD CONSTRAINT pk_$tableName PRIMARY KEY (${"id".inProperCase()})", t.id.ddl[1])
-            assertEquals(1, currentDialectTest.tableColumns(t)[t]!!.size)
-            SchemaUtils.createMissingTablesAndColumns(t)
-            assertEquals(2, currentDialectTest.tableColumns(t)[t]!!.size)
-            SchemaUtils.drop(t)
-        }
-
-        withDb(TestDB.SQLITE) {
-            try {
-                SchemaUtils.createMissingTablesAndColumns(t)
-                assertFalse(db.supportsAlterTableWithAddColumn)
-            } catch (e: SQLException) {
-                // SQLite doesn't support
-            } finally {
-                SchemaUtils.drop(t)
-            }
-        }
-
         withTables(excludeSettings = listOf(TestDB.H2, TestDB.H2_MYSQL, TestDB.SQLITE), tables = arrayOf(initialTable)) {
             assertEquals("ALTER TABLE ${tableName.inProperCase()} ADD ${"id".inProperCase()} ${t.id.columnType.sqlType()} PRIMARY KEY", t.id.ddl)
             assertEquals(1, currentDialectTest.tableColumns(t)[t]!!.size)