diff --git a/datasette/utils/__init__.py b/datasette/utils/__init__.py
index ddd9df8d..47ca0551 100644
--- a/datasette/utils/__init__.py
+++ b/datasette/utils/__init__.py
@@ -187,7 +187,9 @@ allowed_pragmas = (
 disallawed_sql_res = [
     (
         re.compile(f"pragma(?!_({'|'.join(allowed_pragmas)}))"),
-        "Statement may not contain PRAGMA",
+        "Statement contained a disallowed PRAGMA. Allowed pragma functions are {}".format(
+            ", ".join("pragma_{}()".format(pragma) for pragma in allowed_pragmas)
+        ),
     )
 ]
 
diff --git a/docs/sql_queries.rst b/docs/sql_queries.rst
index 74e1e4e5..93f17eaf 100644
--- a/docs/sql_queries.rst
+++ b/docs/sql_queries.rst
@@ -50,10 +50,7 @@ SQLite string escaping rules will be applied to values passed using named
 parameters - they will be wrapped in quotes and their content will be correctly
 escaped.
 
-Datasette disallows custom SQL containing the string PRAGMA, as SQLite pragma
-statements can be used to change database settings at runtime. If you need to
-include the string "pragma" in a query you can do so safely using a named
-parameter.
+Datasette disallows custom SQL queries containing the string PRAGMA (with a small number `of exceptions <https://github.com/simonw/datasette/issues/761>`__) as SQLite pragma statements can be used to change database settings at runtime. If you need to include the string "pragma" in a query you can do so safely using a named parameter.
 
 .. _sql_views:
 
diff --git a/tests/test_html.py b/tests/test_html.py
index e1bcf4d3..c7dd9d97 100644
--- a/tests/test_html.py
+++ b/tests/test_html.py
@@ -1,4 +1,5 @@
 from bs4 import BeautifulSoup as Soup
+from datasette.utils import allowed_pragmas
 from .fixtures import (  # noqa
     app_client,
     app_client_base_url_prefix,
@@ -124,6 +125,20 @@ def test_invalid_custom_sql(app_client):
     assert "Statement must be a SELECT" in response.text
 
 
+def test_disallowed_custom_sql_pragma(app_client):
+    response = app_client.get(
+        "/fixtures?sql=SELECT+*+FROM+pragma_not_on_allow_list('idx52')"
+    )
+    assert response.status == 400
+    pragmas = ", ".join("pragma_{}()".format(pragma) for pragma in allowed_pragmas)
+    assert (
+        "Statement contained a disallowed PRAGMA. Allowed pragma functions are {}".format(
+            pragmas
+        )
+        in response.text
+    )
+
+
 def test_sql_time_limit(app_client_shorter_time_limit):
     response = app_client_shorter_time_limit.get("/fixtures?sql=select+sleep(0.5)")
     assert 400 == response.status