diff --git a/conservancy_beancount/filters.py b/conservancy_beancount/filters.py
index 107f9f470e803197806733e145ec76e02c7a2b73..a7a2b2311bcf3bdd79c4152ba816ccb6773296e9 100644
--- a/conservancy_beancount/filters.py
+++ b/conservancy_beancount/filters.py
@@ -87,5 +87,12 @@ def remove_opening_balance_txn(entries: Entries) -> Optional[Transaction]:
                 break
     else:
         return None
-    del entries[index]
+    # Deleting from the beginning of a list is O(n) slow in Python:
+    # <https://wiki.python.org/moin/TimeComplexity>
+    # So don't do that, and instead replace the transaction with a placeholder
+    # directive.
+    # The type:ignore is because of the funny way Beancount builds directives.
+    entries[index] = bc_data.Custom(  # type:ignore[operator]
+        entry.meta, entry.date, "Removed opening balances", [],
+    )
     return entry
diff --git a/tests/test_filters.py b/tests/test_filters.py
index 9ba4bc4ddf538b5080972676d7a3996a7f8e8f40..ca83d74749d32f0321a923bce15cbf13e228c16c 100644
--- a/tests/test_filters.py
+++ b/tests/test_filters.py
@@ -153,5 +153,9 @@ def test_remove_opening_balance_txn(opening_txn):
         entries.insert(1, opening_txn)
     actual = filters.remove_opening_balance_txn(entries)
     assert actual is opening_txn
-    assert len(entries) == 2
     assert opening_txn not in entries
+    assert not any(
+        post.account.startswith('Equity:')
+        for entry in entries
+        for post in getattr(entry, 'postings', ())
+    )