diff --git a/crates/engine/src/cmd/objects/arrange.rs b/crates/engine/src/cmd/objects/arrange.rs
index abdc85695a..15cc5555d7 100644
--- a/crates/engine/src/cmd/objects/arrange.rs
+++ b/crates/engine/src/cmd/objects/arrange.rs
@@ -147,7 +147,8 @@ pub(super) fn move_object(s: &mut Session, pos: Pos, page: Option<u64>, x: f32,
 }
 
 /// [`move_object`]'s one placement: move the object's character to the anchor under (x, y) on
-/// `page` and offset it from there.
+/// `page` and offset it from there. Objects in headers/footers, on pages without anchoring text,
+/// or configured not to move with text retain page-relative anchoring.
 fn move_object_once(s: &mut Session, pos: &Pos, page: usize, x: f32, y: f32, (w, h): (f32, f32)) -> Result<Pos, CmdError> {
     use wordcraft_doc::para::Anchor;
     if pos.path.depth() > 0 || !movable_story(s, pos.story) {
@@ -164,6 +165,8 @@ fn move_object_once(s: &mut Session, pos: &Pos, page: usize, x: f32, y: f32, (w,
         Some(path) => (Pos { story, path, off: 0 }, false),
         None => (nearest_line(&layout, page, y, story).ok_or_else(|| CmdError::Params("no text on that page to anchor to".into()))?, true),
     };
+    let was_with_text =
+        s.doc.para_at(pos).and_then(|p| p.object_at(pos.off)).and_then(|o| o.frame()).map_or(story == StoryRef::Body, |(_, _, f)| moves_with_text(f));
     // Move its character to the anchor, unless it's already in that paragraph and drawn on this
     // page (one anchored on a later page of it is drawn there, #4250).
     let at = if anchor.story == pos.story && anchor.path == pos.path && !on_page && layout.object(pos, page).is_some_and(|o| o.page == page) {
@@ -196,7 +199,7 @@ fn move_object_once(s: &mut Session, pos: &Pos, page: usize, x: f32, y: f32, (w,
         f.x = x.clamp(-MAX_OFFSET, MAX_OFFSET);
         f.y = y.clamp(-MAX_OFFSET, MAX_OFFSET);
     })?;
-    if on_page {
+    if on_page || story != StoryRef::Body || !was_with_text {
         return Ok(at);
     }
     // Then offsets from its paragraph, as laid out with the object there.
@@ -223,16 +226,23 @@ pub(super) fn unalign(s: &mut Session) -> Result<(), CmdError> {
         return Ok(());
     }
     let hit = s.layout().object(&pos, s.page_hint).ok_or_else(|| CmdError::Failed("the object isn't laid out".into()))?;
-    let (ox, oy) = (hit.rect.x - hit.origin.x, hit.rect.y - hit.origin.y);
+    let (ox, oy) = (
+        if float.h_rel == Anchor::Page { hit.rect.x } else { hit.rect.x - hit.origin.x },
+        if float.v_rel == Anchor::Page { hit.rect.y } else { hit.rect.y - hit.origin.y },
+    );
     edit_float(s, &pos, |f| {
         if f.h_align.is_some() {
             f.h_align = None;
-            f.h_rel = Anchor::Column;
+            if f.h_rel != Anchor::Page {
+                f.h_rel = Anchor::Column;
+            }
             f.x = ox.clamp(-MAX_OFFSET, MAX_OFFSET);
         }
         if f.v_align.is_some() {
             f.v_align = None;
-            f.v_rel = Anchor::Paragraph;
+            if f.v_rel != Anchor::Page {
+                f.v_rel = Anchor::Paragraph;
+            }
             f.y = oy.clamp(-MAX_OFFSET, MAX_OFFSET);
         }
     })?;
diff --git a/crates/engine/src/cmd/objects/tests.rs b/crates/engine/src/cmd/objects/tests.rs
index 13836d60c5..cf302543ac 100644
--- a/crates/engine/src/cmd/objects/tests.rs
+++ b/crates/engine/src/cmd/objects/tests.rs
@@ -1254,6 +1254,165 @@ fn header_pictures_can_be_resized_and_dragged() {
     s.run("edit.undo", &json!({})).unwrap();
     let u = s.layout().object(&selected(&s).unwrap().0, 0).expect("laid out");
     assert!((u.rect.x - 200.0).abs() < 1.0 && (u.rect.y - 60.0).abs() < 1.0, "{:?}", u.rect);
+    let float = selected(&s).unwrap().1.frame().unwrap().2.clone();
+    assert_eq!((float.h_rel, float.v_rel), (wordcraft_doc::para::Anchor::Page, wordcraft_doc::para::Anchor::Page));
+    assert_eq!((float.x, float.y), (200.0, 60.0));
+}
+
+/// #5812: arrange.bounds on a header picture (or after moveWithText false) keeps page anchoring
+/// and exports a page-anchored frame in .odt with coordinates relative to the page.
+#[test]
+fn arrange_bounds_on_header_picture_writes_page_anchored_odt_frame() {
+    use wordcraft_doc::para::Anchor;
+    let mut s = Session::new(wordcraft_doc::Document::new());
+    s.run("insert.editHeader", &json!({})).unwrap();
+    let data = super::super::insert::base64_encode(&png(20, 10));
+    s.run("insert.picture", &json!({"data": data, "width": 100})).unwrap();
+    s.run("arrange.wrap", &json!({"wrap": "square"})).unwrap();
+    s.run("arrange.bounds", &json!({"x": 0.0, "y": 0.0, "page": 0})).unwrap();
+    let float = selected(&s).unwrap().1.frame().unwrap().2.clone();
+    assert_eq!((float.h_rel, float.v_rel), (Anchor::Page, Anchor::Page));
+    assert_eq!((float.x, float.y), (0.0, 0.0));
+
+    let mut z = zip::ZipArchive::new(std::io::Cursor::new(wordcraft_formats::odt::export(&s.doc).unwrap())).unwrap();
+    let mut styles = String::new();
+    std::io::Read::read_to_string(&mut z.by_name("styles.xml").unwrap(), &mut styles).unwrap();
+    assert!(styles.contains(r#"text:anchor-type="page""#), "frame should be page-anchored: {styles}");
+    assert!(styles.contains(r#"svg:x="0pt""#) && styles.contains(r#"svg:y="0pt""#), "offsets should be 0pt: {styles}");
+    assert!(!styles.contains(r#"text:anchor-type="paragraph""#), "frame should not be paragraph-anchored: {styles}");
+
+    // Also test after arrange.moveWithText false
+    s.run("arrange.moveWithText", &json!({"value": false})).unwrap();
+    s.run("arrange.bounds", &json!({"x": 10.0, "y": 20.0, "page": 0})).unwrap();
+    let float = selected(&s).unwrap().1.frame().unwrap().2.clone();
+    assert_eq!((float.h_rel, float.v_rel), (Anchor::Page, Anchor::Page));
+    assert_eq!((float.x, float.y), (10.0, 20.0));
+
+    let mut z = zip::ZipArchive::new(std::io::Cursor::new(wordcraft_formats::odt::export(&s.doc).unwrap())).unwrap();
+    let mut styles = String::new();
+    std::io::Read::read_to_string(&mut z.by_name("styles.xml").unwrap(), &mut styles).unwrap();
+    assert!(styles.contains(r#"text:anchor-type="page""#), "{styles}");
+    assert!(styles.contains(r#"svg:x="10pt""#) && styles.contains(r#"svg:y="20pt""#), "{styles}");
+}
+
+/// Turning off `moveWithText` on a body picture anchors it to the page, and subsequent
+/// `arrange.bounds` retains page-relative anchoring and writes a page-anchored ODT frame.
+#[test]
+fn body_picture_with_move_with_text_false_retains_page_anchor_and_coordinates() {
+    use wordcraft_doc::para::Anchor;
+    let mut s = Session::new(wordcraft_doc::Document::new());
+    s.run("text.insert", &json!({"text": "First line of paragraph.\n"})).unwrap();
+    let data = super::super::insert::base64_encode(&png(20, 10));
+    s.run("insert.picture", &json!({"data": data, "width": 100})).unwrap();
+    s.run("arrange.wrap", &json!({"wrap": "square"})).unwrap();
+    // Default body float moves with text
+    let (_pos, obj) = selected(&s).unwrap();
+    let float = obj.frame().unwrap().2;
+    assert_eq!((float.h_rel, float.v_rel), (Anchor::Column, Anchor::Column));
+
+    // Turn off moveWithText
+    s.run("arrange.moveWithText", &json!({"value": false})).unwrap();
+    let (_, obj) = selected(&s).unwrap();
+    let float = obj.frame().unwrap().2;
+    assert_eq!((float.h_rel, float.v_rel), (Anchor::Column, Anchor::Page));
+
+    // Now call arrange.bounds on a page where a paragraph starts
+    s.run("arrange.bounds", &json!({"page": 0, "x": 50.0, "y": 80.0})).unwrap();
+    let (_, obj) = selected(&s).unwrap();
+    let float = obj.frame().unwrap().2;
+    assert_eq!((float.h_rel, float.v_rel), (Anchor::Page, Anchor::Page));
+    assert_eq!((float.x, float.y), (50.0, 80.0));
+
+    let mut z = zip::ZipArchive::new(std::io::Cursor::new(wordcraft_formats::odt::export(&s.doc).unwrap())).unwrap();
+    let mut content = String::new();
+    std::io::Read::read_to_string(&mut z.by_name("content.xml").unwrap(), &mut content).unwrap();
+    assert!(content.contains(r#"text:anchor-type="page""#), "body picture should export with page anchor: {content}");
+    assert!(content.contains(r#"svg:x="50pt""#) && content.contains(r#"svg:y="80pt""#), "{content}");
+}
+
+/// Changing `moveWithText` on an object with `h_align` set preserves its horizontal
+/// anchor relation and layout position without displacement.
+#[test]
+fn move_with_text_preserves_horizontal_position_when_h_align_set() {
+    use wordcraft_doc::para::{Anchor, FloatAlign};
+    let mut s = Session::new(wordcraft_doc::Document::new());
+    s.run("text.insert", &json!({"text": "First body paragraph with some text.\n"})).unwrap();
+    let data = super::super::insert::base64_encode(&png(20, 10));
+    s.run("insert.picture", &json!({"data": data, "width": 100})).unwrap();
+    s.run("arrange.wrap", &json!({"wrap": "square"})).unwrap();
+
+    // Set horizontal alignment to End (right)
+    let (pos, _) = selected(&s).unwrap();
+    super::select::edit_float(&mut s, &pos, |f| {
+        f.h_align = Some(FloatAlign::End);
+        f.h_rel = Anchor::Margin;
+    })
+    .unwrap();
+    s.touch();
+
+    let hit_before = s.layout().object(&pos, 0).unwrap();
+    let x_before = hit_before.rect.x;
+
+    // Toggle moveWithText false
+    s.run("arrange.moveWithText", &json!({"value": false})).unwrap();
+    let (pos, obj) = selected(&s).unwrap();
+    let float = obj.frame().unwrap().2;
+    assert_eq!(float.v_rel, Anchor::Page);
+    assert_eq!(float.h_align, Some(FloatAlign::End));
+    assert_eq!(float.h_rel, Anchor::Margin);
+    s.touch();
+    let hit_after = s.layout().object(&pos, 0).unwrap();
+    assert!((hit_after.rect.x - x_before).abs() < 0.01, "{:?} vs {:?}", hit_after.rect.x, x_before);
+
+    // Toggle moveWithText true
+    s.run("arrange.moveWithText", &json!({"value": true})).unwrap();
+    let (pos, obj) = selected(&s).unwrap();
+    let float = obj.frame().unwrap().2;
+    assert_eq!(float.v_rel, Anchor::Paragraph);
+    assert_eq!(float.h_align, Some(FloatAlign::End));
+    assert_eq!(float.h_rel, Anchor::Margin);
+    s.touch();
+    let hit_after2 = s.layout().object(&pos, 0).unwrap();
+    assert!((hit_after2.rect.x - x_before).abs() < 0.01, "{:?} vs {:?}", hit_after2.rect.x, x_before);
+}
+
+/// Toggling `moveWithText` preserves horizontal anchor relations (`Margin`, `RightMargin`,
+/// `Character`, `Column`, `Page`) and offset when the object has no horizontal alignment.
+#[test]
+fn move_with_text_preserves_horizontal_anchor_relations_without_alignment() {
+    use wordcraft_doc::para::Anchor;
+    for rel in [Anchor::Margin, Anchor::RightMargin, Anchor::Character, Anchor::Column, Anchor::Page] {
+        let mut s = Session::new(wordcraft_doc::Document::new());
+        s.run("text.insert", &json!({"text": "A line of body text.\n"})).unwrap();
+        let data = super::super::insert::base64_encode(&png(20, 10));
+        s.run("insert.picture", &json!({"data": data, "width": 100})).unwrap();
+        s.run("arrange.wrap", &json!({"wrap": "square"})).unwrap();
+
+        let (pos, _) = selected(&s).unwrap();
+        super::select::edit_float(&mut s, &pos, |f| {
+            f.h_align = None;
+            f.h_rel = rel;
+            f.x = 35.0;
+        })
+        .unwrap();
+        s.touch();
+
+        // Toggle moveWithText false
+        s.run("arrange.moveWithText", &json!({"value": false})).unwrap();
+        let (_, obj) = selected(&s).unwrap();
+        let float = obj.frame().unwrap().2;
+        assert_eq!(float.v_rel, Anchor::Page, "expected Page v_rel for {rel:?}");
+        assert_eq!(float.h_rel, rel, "expected {rel:?} preserved on moveWithText false");
+        assert!((float.x - 35.0).abs() < 0.01, "expected x preserved on moveWithText false");
+
+        // Toggle moveWithText true
+        s.run("arrange.moveWithText", &json!({"value": true})).unwrap();
+        let (_, obj) = selected(&s).unwrap();
+        let float = obj.frame().unwrap().2;
+        assert_eq!(float.v_rel, Anchor::Paragraph, "expected Paragraph v_rel for {rel:?}");
+        assert_eq!(float.h_rel, rel, "expected {rel:?} preserved on moveWithText true");
+        assert!((float.x - 35.0).abs() < 0.01, "expected x preserved on moveWithText true");
+    }
 }
 
 /// Shape Format › Text (#369): direction and alignment on the box the caret is in, then
diff --git a/crates/formats/src/odt/frames.rs b/crates/formats/src/odt/frames.rs
index 51accf7fb8..0d13c7a874 100644
--- a/crates/formats/src/odt/frames.rs
+++ b/crates/formats/src/odt/frames.rs
@@ -576,7 +576,9 @@ pub(super) fn turned(f: &Float) -> bool {
 
 /// How a floating picture is written: its `text:anchor-type`, its graphic style's
 /// `style:graphic-properties` attributes, and the frame's `svg:x`/`svg:y` attributes, or its
-/// `draw:transform` when it is turned (`w` × `h` its size).
+/// `draw:transform` when it is turned (`w` × `h` its size). Frames anchored to the page on both
+/// horizontal and vertical axes export with `page` anchor; mixed or paragraph-relative frames
+/// export with `paragraph` (or `char` for line-relative vertical) anchor to preserve placement.
 pub(super) fn frame_of(f: &Float, w: f32, h: f32) -> (&'static str, String, String) {
     // A page number holds until it is placed by its paragraph: moved in WordCraft.
     let by_paragraph =
diff --git a/crates/formats/src/odt/tests_more/headers.rs b/crates/formats/src/odt/tests_more/headers.rs
index 80478447d4..595abc2838 100644
--- a/crates/formats/src/odt/tests_more/headers.rs
+++ b/crates/formats/src/odt/tests_more/headers.rs
@@ -395,3 +395,82 @@ fn libreoffices_watermark_reads_as_the_watermark() {
     let [w, h] = wm.size.unwrap();
     assert!((w - 6.69 * 72.0).abs() < 0.5 && (h - 2.24 * 72.0).abs() < 0.5);
 }
+
+/// A picture in a header anchored to the page on both axes exports as a page-anchored
+/// ODT frame with matching coordinates and round-trips with page-relative relations.
+#[test]
+fn a_page_anchored_picture_in_a_header_exports_with_page_anchor() {
+    let mut d = Document::new();
+    d.body = vec![text_para("Body", Default::default())];
+    let pic = {
+        let img = image::RgbaImage::from_fn(4, 4, |_, _| image::Rgba([10, 20, 30, 255]));
+        let mut png = Vec::new();
+        img.write_to(&mut std::io::Cursor::new(&mut png), image::ImageFormat::Png).unwrap();
+        png
+    };
+    let media = d.add_media(pic, "png");
+    let float = wordcraft_doc::para::Float {
+        wrap: wordcraft_doc::para::Wrap::Square,
+        h_rel: wordcraft_doc::para::Anchor::Page,
+        v_rel: wordcraft_doc::para::Anchor::Page,
+        x: 0.0,
+        y: 0.0,
+        ..Default::default()
+    };
+    let mut hp = Paragraph::new();
+    hp.text = wordcraft_doc::para::OBJ.into();
+    hp.objects.push(InlineObject::Image { media, w: 100.0, h: 50.0, alt: "pic".into(), float, crop: [0.0; 4], fx: Default::default(), ole: None });
+    hp.runs = vec![wordcraft_doc::para::Run { len: hp.text.len(), props: Default::default() }];
+    d.parts.insert(1, part(PartKind::Header, vec![para_block(hp)]));
+    d.last_section.headers.default = Some(1);
+
+    let saved = export(&d).unwrap();
+    let styles = crate::odt::tests::entry(&saved, "styles.xml");
+    assert!(styles.contains(r#"text:anchor-type="page""#), "{styles}");
+    assert!(styles.contains(r#"svg:x="0pt""#) && styles.contains(r#"svg:y="0pt""#), "{styles}");
+    assert!(!styles.contains(r#"text:anchor-type="paragraph""#), "{styles}");
+
+    let back = import(&saved).unwrap();
+    let h = back.parts.get(&back.last_section.headers.default.unwrap()).unwrap().blocks[0].as_para().unwrap();
+    let InlineObject::Image { float, .. } = &h.objects[0] else { panic!("not an image") };
+    assert_eq!((float.h_rel, float.v_rel, float.x, float.y), (wordcraft_doc::para::Anchor::Page, wordcraft_doc::para::Anchor::Page, 0.0, 0.0));
+}
+
+/// Mixed page-relative and paragraph/line/char anchor relations export with the proper
+/// anchor type and retain placement and anchor relationships through ODT export and import.
+#[test]
+fn mixed_anchor_relations_preserve_placement_and_roundtrip() {
+    for (h_rel, v_rel, expected_anchor, expected_hrel, expected_vrel) in [
+        (wordcraft_doc::para::Anchor::Page, wordcraft_doc::para::Anchor::Paragraph, "paragraph", "page", "paragraph"),
+        (wordcraft_doc::para::Anchor::Column, wordcraft_doc::para::Anchor::Page, "paragraph", "paragraph-content", "page"),
+        (wordcraft_doc::para::Anchor::Character, wordcraft_doc::para::Anchor::Page, "paragraph", "char", "page"),
+        (wordcraft_doc::para::Anchor::Page, wordcraft_doc::para::Anchor::Line, "char", "page", "line"),
+    ] {
+        let mut d = Document::new();
+        let pic = {
+            let img = image::RgbaImage::from_fn(4, 4, |_, _| image::Rgba([10, 20, 30, 255]));
+            let mut png = Vec::new();
+            img.write_to(&mut std::io::Cursor::new(&mut png), image::ImageFormat::Png).unwrap();
+            png
+        };
+        let media = d.add_media(pic, "png");
+        let float = wordcraft_doc::para::Float { wrap: wordcraft_doc::para::Wrap::Square, h_rel, v_rel, x: 15.0, y: 25.0, ..Default::default() };
+        let mut p = Paragraph::new();
+        p.text = wordcraft_doc::para::OBJ.into();
+        p.objects.push(InlineObject::Image { media, w: 100.0, h: 50.0, alt: "pic".into(), float, crop: [0.0; 4], fx: Default::default(), ole: None });
+        p.runs = vec![wordcraft_doc::para::Run { len: p.text.len(), props: Default::default() }];
+        d.body = vec![para_block(p)];
+
+        let saved = export(&d).unwrap();
+        let content = crate::odt::tests::entry(&saved, "content.xml");
+        assert!(content.contains(&format!(r#"text:anchor-type="{expected_anchor}""#)), "missing {expected_anchor}: {content}");
+        assert!(content.contains(&format!(r#"style:horizontal-rel="{expected_hrel}""#)), "missing {expected_hrel}: {content}");
+        assert!(content.contains(&format!(r#"style:vertical-rel="{expected_vrel}""#)), "missing {expected_vrel}: {content}");
+
+        let back = import(&saved).unwrap();
+        let p_back = back.body[0].as_para().unwrap();
+        let InlineObject::Image { float: back_float, .. } = &p_back.objects[0] else { panic!("not an image") };
+        assert_eq!((back_float.h_rel, back_float.v_rel), (h_rel, v_rel));
+        assert!((back_float.x - 15.0).abs() < 0.01 && (back_float.y - 25.0).abs() < 0.01, "{back_float:?}");
+    }
+}