diff --git a/migration_checker/executor.py b/migration_checker/executor.py
index 0a7c4f8..b88ae73 100644
--- a/migration_checker/executor.py
+++ b/migration_checker/executor.py
@@ -2,13 +2,15 @@
 Helper to execute migrations and record results
 """
 
-from typing import Any, Callable, Union, cast
+from typing import Any, Callable, Sequence, Union, cast
 
 import django
+import sqlparse  # type: ignore[import]
 from django.contrib.postgres.operations import NotInTransactionMixin
 from django.db import connections, transaction
-from django.db.migrations import Migration
+from django.db.migrations import Migration, RunSQL, SeparateDatabaseAndState
 from django.db.migrations.executor import MigrationExecutor
+from django.db.migrations.operations.base import Operation
 from django.db.migrations.recorder import MigrationRecorder
 from django.db.migrations.state import ProjectState
 
@@ -43,7 +45,7 @@ def __init__(
         *,
         database: str,
         apply_migrations: bool,
-        outputs: list[Union[ConsoleOutput, GithubCommentOutput]]
+        outputs: list[Union[ConsoleOutput, GithubCommentOutput]],
     ) -> None:
         self.database = database
         self.apply_migrations = apply_migrations
@@ -118,11 +120,7 @@ def _apply_migration(
         # Some operations, like AddIndexConcurrently, cannot be run in a
         # transaction, so for those special cases we skip recording locks
         # because we ahave no way of doing that.
-        must_be_non_atomic = any(
-            isinstance(operation, NotInTransactionMixin)
-            for operation in migration.operations
-        )
-        if must_be_non_atomic:
+        if self._must_be_non_atomic(migration.operations):
             return self._apply_non_atomic_migration(migration, state), None
 
         # Apply the migration in the database and record queries and locks
@@ -137,6 +135,58 @@ def _apply_migration(
 
         return query_logger.queries, locks
 
+    def _must_be_non_atomic_query(self, query: str) -> bool:
+        """
+        Try to detect if a raw query must be non-atomic.
+        """
+
+        patterns = [
+            [
+                (sqlparse.tokens.DDL, "CREATE"),
+                (sqlparse.tokens.Keyword, "INDEX"),
+                (sqlparse.tokens.Keyword, "CONCURRENTLY"),
+            ],
+            [
+                (sqlparse.tokens.DDL, "DROP"),
+                (sqlparse.tokens.Keyword, "INDEX"),
+                (sqlparse.tokens.Keyword, "CONCURRENTLY"),
+            ],
+        ]
+
+        for statement in sqlparse.parse(query):
+            for pattern in patterns:
+                if all(
+                    any(token.match(ttype, value) for token in statement.tokens)
+                    for ttype, value in pattern
+                ):
+                    return True
+        return False
+
+    def _must_be_non_atomic(self, operations: Sequence[Operation]) -> bool:
+        """
+        Check if any of the operations must be run outside of a transaction.
+        This is the case for some operations, like AddIndexConcurrently. This
+        will recursivey check SeparateDatabaseAndState migrations.
+        """
+
+        for operation in operations:
+            if isinstance(operation, NotInTransactionMixin):
+                return True
+            if isinstance(operation, SeparateDatabaseAndState):
+                return self._must_be_non_atomic(operation.database_operations)
+            if isinstance(operation, RunSQL):
+                if isinstance(operation.sql, str):
+                    return self._must_be_non_atomic_query(operation.sql)
+                else:
+                    return any(
+                        self._must_be_non_atomic_query(statement)
+                        if isinstance(statement, str)
+                        else self._must_be_non_atomic_query(statement[0])
+                        for statement in operation.sql
+                    )
+
+        return False
+
     def _apply_non_atomic_migration(
         self, migration: Migration, state: ProjectState
     ) -> list[str]:
diff --git a/poetry.lock b/poetry.lock
index 3b2de11..f421062 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,10 +1,9 @@
-# This file is automatically @generated by Poetry and should not be changed by hand.
+# This file is automatically @generated by Poetry 1.5.1 and should not be changed by hand.
 
 [[package]]
 name = "asgiref"
 version = "3.6.0"
 description = "ASGI specs, helper code, and adapters"
-category = "main"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -19,7 +18,6 @@ tests = ["mypy (>=0.800)", "pytest", "pytest-asyncio"]
 name = "attrs"
 version = "22.2.0"
 description = "Classes Without Boilerplate"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -38,7 +36,6 @@ tests-no-zope = ["cloudpickle", "cloudpickle", "hypothesis", "hypothesis", "mypy
 name = "black"
 version = "23.1.0"
 description = "The uncompromising code formatter."
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -88,7 +85,6 @@ uvloop = ["uvloop (>=0.15.2)"]
 name = "click"
 version = "8.1.3"
 description = "Composable command line interface toolkit"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -103,7 +99,6 @@ colorama = {version = "*", markers = "platform_system == \"Windows\""}
 name = "colorama"
 version = "0.4.6"
 description = "Cross-platform colored terminal text."
-category = "dev"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,!=3.6.*,>=2.7"
 files = [
@@ -115,7 +110,6 @@ files = [
 name = "django"
 version = "4.1.6"
 description = "A high-level Python web framework that encourages rapid development and clean, pragmatic design."
-category = "main"
 optional = false
 python-versions = ">=3.8"
 files = [
@@ -136,7 +130,6 @@ bcrypt = ["bcrypt"]
 name = "django-stubs"
 version = "1.14.0"
 description = "Mypy stubs for Django"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -160,7 +153,6 @@ compatible-mypy = ["mypy (>=0.991,<1.0)"]
 name = "django-stubs-ext"
 version = "0.7.0"
 description = "Monkey-patching and extensions for django-stubs"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -176,7 +168,6 @@ typing-extensions = "*"
 name = "exceptiongroup"
 version = "1.1.0"
 description = "Backport of PEP 654 (exception groups)"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -191,7 +182,6 @@ test = ["pytest (>=6)"]
 name = "flake8"
 version = "6.0.0"
 description = "the modular source code checker: pep8 pyflakes and co"
-category = "dev"
 optional = false
 python-versions = ">=3.8.1"
 files = [
@@ -208,7 +198,6 @@ pyflakes = ">=3.0.0,<3.1.0"
 name = "iniconfig"
 version = "2.0.0"
 description = "brain-dead simple config-ini parsing"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -220,7 +209,6 @@ files = [
 name = "isort"
 version = "5.12.0"
 description = "A Python utility / library to sort Python imports."
-category = "dev"
 optional = false
 python-versions = ">=3.8.0"
 files = [
@@ -238,7 +226,6 @@ requirements-deprecated-finder = ["pip-api", "pipreqs"]
 name = "mccabe"
 version = "0.7.0"
 description = "McCabe checker, plugin for flake8"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -250,7 +237,6 @@ files = [
 name = "mypy"
 version = "1.0.0"
 description = "Optional static typing for Python"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -297,7 +283,6 @@ reports = ["lxml"]
 name = "mypy-extensions"
 version = "1.0.0"
 description = "Type system extensions for programs checked with the mypy type checker."
-category = "dev"
 optional = false
 python-versions = ">=3.5"
 files = [
@@ -309,7 +294,6 @@ files = [
 name = "packaging"
 version = "23.0"
 description = "Core utilities for Python packages"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -321,7 +305,6 @@ files = [
 name = "pathspec"
 version = "0.11.0"
 description = "Utility library for gitignore style pattern matching of file paths."
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -333,7 +316,6 @@ files = [
 name = "platformdirs"
 version = "3.0.0"
 description = "A small Python package for determining appropriate platform-specific dirs, e.g. a \"user data dir\"."
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -349,7 +331,6 @@ test = ["appdirs (==1.4.4)", "covdefaults (>=2.2.2)", "pytest (>=7.2.1)", "pytes
 name = "pluggy"
 version = "1.0.0"
 description = "plugin and hook calling mechanisms for python"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -365,7 +346,6 @@ testing = ["pytest", "pytest-benchmark"]
 name = "psycopg2"
 version = "2.9.5"
 description = "psycopg2 - Python-PostgreSQL Database Adapter"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -388,7 +368,6 @@ files = [
 name = "pycodestyle"
 version = "2.10.0"
 description = "Python style guide checker"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -400,7 +379,6 @@ files = [
 name = "pyflakes"
 version = "3.0.1"
 description = "passive checker of Python programs"
-category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
@@ -412,7 +390,6 @@ files = [
 name = "pytest"
 version = "7.2.1"
 description = "pytest: simple powerful testing with Python"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -434,21 +411,24 @@ testing = ["argcomplete", "hypothesis (>=3.56)", "mock", "nose", "pygments (>=2.
 
 [[package]]
 name = "sqlparse"
-version = "0.4.3"
+version = "0.4.4"
 description = "A non-validating SQL parser."
-category = "main"
 optional = false
 python-versions = ">=3.5"
 files = [
-    {file = "sqlparse-0.4.3-py3-none-any.whl", hash = "sha256:0323c0ec29cd52bceabc1b4d9d579e311f3e4961b98d174201d5622a23b85e34"},
-    {file = "sqlparse-0.4.3.tar.gz", hash = "sha256:69ca804846bb114d2ec380e4360a8a340db83f0ccf3afceeb1404df028f57268"},
+    {file = "sqlparse-0.4.4-py3-none-any.whl", hash = "sha256:5430a4fe2ac7d0f93e66f1efc6e1338a41884b7ddf2a350cedd20ccc4d9d28f3"},
+    {file = "sqlparse-0.4.4.tar.gz", hash = "sha256:d446183e84b8349fa3061f0fe7f06ca94ba65b426946ffebe6e3e8295332420c"},
 ]
 
+[package.extras]
+dev = ["build", "flake8"]
+doc = ["sphinx"]
+test = ["pytest", "pytest-cov"]
+
 [[package]]
 name = "tomli"
 version = "2.0.1"
 description = "A lil' TOML parser"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -460,7 +440,6 @@ files = [
 name = "types-pytz"
 version = "2022.7.1.0"
 description = "Typing stubs for pytz"
-category = "dev"
 optional = false
 python-versions = "*"
 files = [
@@ -472,7 +451,6 @@ files = [
 name = "types-pyyaml"
 version = "6.0.12.5"
 description = "Typing stubs for PyYAML"
-category = "dev"
 optional = false
 python-versions = "*"
 files = [
@@ -484,7 +462,6 @@ files = [
 name = "typing-extensions"
 version = "4.4.0"
 description = "Backported and Experimental Type Hints for Python 3.7+"
-category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
@@ -496,7 +473,6 @@ files = [
 name = "tzdata"
 version = "2022.7"
 description = "Provider of IANA time zone data"
-category = "main"
 optional = false
 python-versions = ">=2"
 files = [
@@ -510,4 +486,4 @@ django = ["Django"]
 [metadata]
 lock-version = "2.0"
 python-versions = "^3.9"
-content-hash = "d9f9054f4c284749ee4abbf2ea36d71e196cee1cdff2dfb87b1207f096652659"
+content-hash = "1b4a84ab1af32c4ab489440c5f976f8b3e9991570c369c494644331d89967311"
diff --git a/pyproject.toml b/pyproject.toml
index d05b6cb..08fadc9 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,6 +11,7 @@ packages = [
 [tool.poetry.dependencies]
 python = "^3.9"
 Django = {version = ">=3.2", optional = true }
+sqlparse = ">=0.3.1"
 
 [tool.poetry.extras]
 django = ["Django"]
diff --git a/tests/test_executor.py b/tests/test_executor.py
index 9055b40..6b9770b 100644
--- a/tests/test_executor.py
+++ b/tests/test_executor.py
@@ -1,3 +1,13 @@
+from unittest.mock import Mock
+
+import pytest
+from django.contrib.postgres.operations import (
+    AddIndexConcurrently,
+    RemoveIndexConcurrently,
+)
+from django.db.migrations import AddIndex, RunSQL, SeparateDatabaseAndState
+from django.db.migrations.operations.base import Operation
+
 from migration_checker.executor import Executor
 from migration_checker.output import ConsoleOutput
 
@@ -7,3 +17,50 @@ def test_executor(setup_db: None) -> None:
         database="default", apply_migrations=True, outputs=[ConsoleOutput()]
     )
     executor.run()
+
+
+@pytest.mark.parametrize(
+    "operation,must_be_non_atomic",
+    [
+        (AddIndex("test", index=Mock()), False),
+        (AddIndexConcurrently("test", index=Mock()), True),
+        (RemoveIndexConcurrently("foo", "test"), True),
+        (RunSQL("CREATE INDEX foobar"), False),
+        (RunSQL("CREATE INDEX foobar CONCURRENTLY", RunSQL.noop), True),
+        (RunSQL("DROP INDEX foobar CONCURRENTLY", RunSQL.noop), True),
+        (RunSQL([("CREATE INDEX foobar", None)]), False),
+        (RunSQL([("CREATE INDEX foobar CONCURRENTLY", None)]), True),
+        (
+            SeparateDatabaseAndState(
+                database_operations=[RunSQL("CREATE INDEX foobar")]
+            ),
+            False,
+        ),
+        (
+            SeparateDatabaseAndState(
+                database_operations=[RunSQL("CREATE INDEX foobar CONCURRENTLY")]
+            ),
+            True,
+        ),
+        (
+            SeparateDatabaseAndState(
+                database_operations=[AddIndex("test", index=Mock())]
+            ),
+            False,
+        ),
+        (
+            SeparateDatabaseAndState(
+                database_operations=[AddIndexConcurrently("test", index=Mock())]
+            ),
+            True,
+        ),
+    ],
+)
+def test_run_sql_must_be_non_atomic(
+    operation: Operation, must_be_non_atomic: bool
+) -> None:
+    executor = Executor(
+        database="default", apply_migrations=True, outputs=[ConsoleOutput()]
+    )
+
+    assert executor._must_be_non_atomic([operation]) is must_be_non_atomic