diff --git a/crates/sign/src/pdf/signing.rs b/crates/sign/src/pdf/signing.rs
index 71dd10b302..b41d7fe91a 100644
--- a/crates/sign/src/pdf/signing.rs
+++ b/crates/sign/src/pdf/signing.rs
@@ -153,6 +153,7 @@ fn sign_inner(
     }
     check_signing_permissions(doc, opts)?;
     let mut doc = doc.clone();
+    let earlier_signatures = !super::validate::signature_contents(&doc).is_empty();
     let root = doc.root().ok_or_else(|| SignError::Pdf("the document has no catalog".into()))?;
     let alg = id.key.preferred_digest();
     let reserve =
@@ -293,6 +294,22 @@ fn sign_inner(
             doc.update_dict(r, |af| af.set(b"SigFlags".to_vec(), Object::Int(3)))?;
         }
     }
+    // Acrobat does not recognise a signature in a form that asks viewers to redraw its fields
+    // (`/NeedAppearances true`): redrawing would change what the signature covers. The first
+    // signature drops the flag; a later one leaves it, as removing it would count as a change
+    // to the earlier signatures.
+    if !earlier_signatures {
+        if let Some(Object::Ref(r)) = doc.get(root).as_dict().and_then(|c| c.get(b"AcroForm").cloned()) {
+            doc.update_dict(r, |af| {
+                af.remove(b"NeedAppearances");
+            })?;
+        }
+        doc.update_dict(root, |c| {
+            if let Some(Object::Dict(af)) = c.get_mut(b"AcroForm") {
+                af.remove(b"NeedAppearances");
+            }
+        })?;
+    }
     // The appearance.
     let ap = appearance(&mut doc, rect, turn, &name, &id.certificate, opts)?;
     let ap_ref = doc.add(Object::Stream(ap));
diff --git a/crates/sign/tests/it/pdf.rs b/crates/sign/tests/it/pdf.rs
index 869a4bebd5..ce4b30de9e 100644
--- a/crates/sign/tests/it/pdf.rs
+++ b/crates/sign/tests/it/pdf.rs
@@ -122,6 +122,56 @@ fn signing_then_validating_with_and_without_trust() {
     }
 }
 
+/// The form dictionary of `bytes`, with the catalog's reference resolved.
+fn form_of(bytes: &[u8]) -> Dict {
+    let doc = open(bytes);
+    let form = doc.get(doc.root().unwrap()).as_dict().and_then(|c| c.get(b"AcroForm").map(|a| doc.resolve(a))).unwrap();
+    form.as_dict().unwrap().clone()
+}
+
+/// A form with `/NeedAppearances true` makes Acrobat ignore the signature (#5939): the first
+/// signature drops the flag, whether the AcroForm is inline or indirect, and leaves the rest of
+/// the form alone.
+#[test]
+fn signing_drops_need_appearances() {
+    let id = pkcs12::open(&data("ec-p256.p12"), "test").unwrap();
+    let inline = fixture_with(b"<< /Type /Catalog /Pages 2 0 R /AcroForm << /Fields [6 0 R] /NeedAppearances true >> >>", &[]);
+    let indirect =
+        fixture_with(b"<< /Type /Catalog /Pages 2 0 R /AcroForm 7 0 R >>", &[b"<< /Fields [6 0 R] /NeedAppearances true /DA (/Helv 0 Tf 0 g) >>"]);
+    for (what, bytes) in [("inline", inline), ("indirect", indirect)] {
+        assert_eq!(form_of(&bytes).get(b"NeedAppearances"), Some(&Object::Bool(true)), "{what}");
+        let signed = pdfcraft_sign::sign(&open(&bytes), &id, &SignOptions { field: Some("Approval".into()), ..opts() }).unwrap();
+        let form = form_of(&signed);
+        assert!(form.get(b"NeedAppearances").is_none(), "{what}");
+        assert_eq!(form.get(b"SigFlags"), Some(&Object::Int(3)), "{what}");
+        assert!(form.get(b"Fields").is_some(), "{what}");
+        let doc = open(&signed);
+        assert!(signatures(&doc, &signed, &TrustStore::default()).iter().any(|s| s.field == "Approval" && s.signed), "{what}");
+    }
+}
+
+/// A second signer leaves the form's flags alone: changing them would count as a change to
+/// what the first signature covered.
+#[test]
+fn a_later_signature_does_not_change_need_appearances() {
+    let id = pkcs12::open(&data("ec-p256.p12"), "test").unwrap();
+    let first = pdfcraft_sign::sign(&open(&fixture()), &id, &SignOptions { field: Some("Approval".into()), ..opts() }).unwrap();
+    let mut doc = open(&first);
+    let root = doc.root().unwrap();
+    doc.update_dict(root, |c| {
+        if let Some(Object::Dict(af)) = c.get_mut(b"AcroForm") {
+            af.set(b"NeedAppearances".to_vec(), Object::Bool(true));
+        }
+    })
+    .unwrap();
+    if let Some(Object::Ref(r)) = doc.get(root).as_dict().and_then(|c| c.get(b"AcroForm").cloned()) {
+        doc.update_dict(r, |af| af.set(b"NeedAppearances".to_vec(), Object::Bool(true))).unwrap();
+    }
+    let flagged = write_incremental(&doc, &SaveOptions { object_streams: false, ..SaveOptions::default() }).unwrap();
+    let second = pdfcraft_sign::sign(&open(&flagged), &id, &opts()).unwrap();
+    assert_eq!(form_of(&second).get(b"NeedAppearances"), Some(&Object::Bool(true)));
+}
+
 #[test]
 fn signing_an_existing_field_and_counter_signing() {
     let id = pkcs12::open(&data("ec-p256.p12"), "test").unwrap();