diff --git a/src/ocrmypdf/_graft.py b/src/ocrmypdf/_graft.py
index 9c3d6574..0ebc63c1 100644
--- a/src/ocrmypdf/_graft.py
+++ b/src/ocrmypdf/_graft.py
@@ -117,6 +117,10 @@ def _build_text_layer_ctm(
 ):
     """Build transformation matrix to align text layer with page content.
 
+    Always computes the full CTM to handle non-zero page origins (e.g.,
+    JSTOR PDFs with MediaBox like [0, 100, 595, 982]) and minor scale
+    differences due to DPI rounding.
+
     Args:
         text_width: Width of text layer mediabox.
         text_height: Height of text layer mediabox.
@@ -127,11 +131,8 @@ def _build_text_layer_ctm(
         text_rotation: Rotation in degrees (clockwise) to apply to text layer.
 
     Returns:
-        pikepdf.Matrix transformation matrix, or None if no rotation needed.
+        pikepdf.Matrix transformation matrix, or None if identity.
     """
-    if text_rotation == 0:
-        return None
-
     from pikepdf import Matrix
 
     wt, ht = text_width, text_height
@@ -153,7 +154,14 @@ def _build_text_layer_ctm(
     scale_y = page_height / ht if ht else 1.0
     scale = Matrix().scaled(scale_x, scale_y)
 
-    return translate @ rotate @ scale @ untranslate @ corner
+    ctm = translate @ rotate @ scale @ untranslate @ corner
+
+    # Return None if the result is effectively identity
+    identity = Matrix()
+    if ctm == identity:
+        return None
+
+    return ctm
 
 
 log = logging.getLogger(__name__)
diff --git a/tests/test_graft.py b/tests/test_graft.py
index 462e1b1c..5c0fbbe1 100644
--- a/tests/test_graft.py
+++ b/tests/test_graft.py
@@ -46,24 +46,19 @@ def test_redo_ocr_with_offset_mediabox(resources, outdir):
     """Test that --redo-ocr handles non-zero mediabox origins correctly.
 
     Regression test for issue #1630 where PDFs with mediabox origins like
-    [0, 100, width, height+100] (common in cropped PDFs)
-    would have OCR text shifted vertically because the Form XObject BBox
-    used the text layer's mediabox [0, 0, w, h] instead of the base page's
-    mediabox [0, 100, w, h+100].
-
-    Before the fix, the BBox would be [0, 0, w, h] but the transformation
-    matrix would expect [0, 100, w, h+100], causing a 100pt vertical shift.
+    [0, 100, width, height+100] (common in cropped/JSTOR-style PDFs)
+    would have OCR text shifted vertically because the text layer CTM
+    did not account for the page origin offset.
     """
     # Create a PDF with a non-zero mediabox origin
     input_pdf = outdir / 'offset_mediabox_input.pdf'
+    y_offset = 100
 
     with pikepdf.open(resources / 'graph_ocred.pdf') as pdf:
         page = pdf.pages[0]
         original_mb = list(page.MediaBox)
 
         # Shift mediabox Y origin to simulate cropped/JSTOR-style PDFs
-        # This is the scenario that triggers the bug
-        y_offset = 100
         page.MediaBox = [
             original_mb[0],
             original_mb[1] + y_offset,
@@ -84,18 +79,15 @@ def test_redo_ocr_with_offset_mediabox(resources, outdir):
 
         # MediaBox origin should be preserved
         assert (
-            float(mediabox[1]) == 100.0
-        ), f"MediaBox Y origin should be preserved at 100, got {mediabox[1]}"
+            float(mediabox[1]) == y_offset
+        ), f"MediaBox Y origin should be preserved at {y_offset}, got {mediabox[1]}"
 
-        # MediaBox should have valid dimensions
-        width = float(mediabox[2]) - float(mediabox[0])
-        height = float(mediabox[3]) - float(mediabox[1])
-        assert width > 0 and height > 0, "MediaBox should have positive dimensions"
-
-        # Page content should be present (may include XObject references
-        # for the OCR text layer and/or inline image operators)
-        text_content = page.Contents.read_bytes()
-        assert len(text_content) > 0, "Page should have content"
+        # The content stream should include a CTM with the Y origin translation.
+        # Without the fix, the CTM was omitted for rotation==0, causing a shift.
+        content = page.Contents.read_bytes()
+        assert b'cm' in content, (
+            "Content stream should include a CTM to translate by the page origin"
+        )
 
 
 def test_strip_invisble_text():