diff --git a/crates/engine/src/cmd/distortcmds.rs b/crates/engine/src/cmd/distortcmds.rs
index 2dbb7a9a18..8f1b5b97e6 100644
--- a/crates/engine/src/cmd/distortcmds.rs
+++ b/crates/engine/src/cmd/distortcmds.rs
@@ -26,7 +26,7 @@ pub use perspective::perspective_click;
 use perspective::{
     attach, edit_text, grid_set, grid_show, persp_draw, persp_move, persp_nudge, persp_transform, plane_match, plane_move, plane_set, release,
 };
-pub(crate) use perspective::{finish_edit_text, grid_of, perspective_rewrite, silent, store_grid, transform_again};
+pub(crate) use perspective::{finish_edit_text, grid_kept, grid_of, perspective_rewrite, silent, store_grid, transform_again};
 
 pub fn specs() -> Vec<CommandSpec> {
     vec![
@@ -107,7 +107,7 @@ pub fn specs() -> Vec<CommandSpec> {
             "Perspective Grid Preset",
             [],
             None,
-            "{kind: 1|2|3 (its normal view) | name: a preset (see perspective.presets.list)} reset the grid to the preset fitted to the first artboard (and show it; attached objects stay attached)",
+            "{kind: 1|2|3 (its normal view) | name: a preset (see perspective.presets.list)} reset the grid to the preset fitted to the first artboard (and show it; attached objects stay attached). No undo step when the document already holds that grid; when only whether it shows or its active plane differs, those are set without one",
             has_doc,
             super::perspgrid::grid_preset
         ),
diff --git a/crates/engine/src/cmd/distortcmds/perspective.rs b/crates/engine/src/cmd/distortcmds/perspective.rs
index 62b72a8e0f..89091248df 100644
--- a/crates/engine/src/cmd/distortcmds/perspective.rs
+++ b/crates/engine/src/cmd/distortcmds/perspective.rs
@@ -18,7 +18,7 @@ pub(crate) fn store_grid(d: &mut Document, g: &PerspectiveGrid) {
 
 /// Whether `d` holds `g` as [`store_grid`] writes it (with `attached` cleared): then storing `g`
 /// leaves `d` as it is.
-fn grid_kept(d: &Document, g: &PerspectiveGrid) -> bool {
+pub(crate) fn grid_kept(d: &Document, g: &PerspectiveGrid) -> bool {
     let mut g = g.clone();
     g.attached.clear();
     serde_json::to_value(&g).is_ok_and(|v| d.unknown.get(persp::DOC_KEY) == Some(&v))
diff --git a/crates/engine/src/cmd/perspgrid.rs b/crates/engine/src/cmd/perspgrid.rs
index d13e7d8c52..aaeee36d80 100644
--- a/crates/engine/src/cmd/perspgrid.rs
+++ b/crates/engine/src/cmd/perspgrid.rs
@@ -19,7 +19,7 @@ use vectorcraft_tools::distort::perspective::widget::{WidgetCorner, WidgetPlace}
 use vectorcraft_tools::distort::perspective::{GridDefinition, PerspectiveGrid};
 use vectorcraft_tools::{PointerEvent, PointerKind, ToolKey};
 
-use super::distortcmds::{grid_of, silent, store_grid};
+use super::distortcmds::{grid_kept, grid_of, silent, store_grid};
 use super::{CommandSpec, EngineError, Result, Session, always, bad, bool_or, cmd, has_doc, str_param, switch_or, unique_name};
 
 pub fn specs() -> Vec<CommandSpec> {
@@ -261,10 +261,21 @@ pub(crate) fn grid_preset(s: &mut Session, p: &Value) -> Result<Value> {
     let g = s.perspective_preset_grid(&name, ab).ok_or_else(|| bad(C, format!("no perspective grid preset named `{name}`")))?;
     // The objects stay attached and the view options stay as they were.
     let g = PerspectiveGrid { attached: old.attached, locked: old.locked, lock_station: old.lock_station, snap: old.snap, rulers: old.rulers, ..g };
-    s.edit("Perspective Grid Preset", |d, _| {
-        store_grid(d, &g);
-        Ok(())
-    })?;
+    // When the document holds this grid already, apart from whether it shows and its active plane,
+    // the preset only sets those two, without an undo step (as perspective.grid.show and
+    // perspective.plane.set do).
+    let view = PerspectiveGrid { visible: old.visible, plane: old.plane, ..g.clone() };
+    if !grid_kept(&s.doc()?.doc, &view) {
+        s.edit("Perspective Grid Preset", |d, _| {
+            store_grid(d, &g);
+            Ok(())
+        })?;
+    } else if (old.visible, old.plane) != (g.visible, g.plane) {
+        silent(s, |cur| {
+            cur.visible = g.visible;
+            cur.plane = g.plane;
+        })?;
+    }
     Ok(g.definition_json())
 }
 
diff --git a/crates/engine/src/tests/perspgrid.rs b/crates/engine/src/tests/perspgrid.rs
index 07fce547da..dce149e98c 100644
--- a/crates/engine/src/tests/perspgrid.rs
+++ b/crates/engine/src/tests/perspgrid.rs
@@ -150,6 +150,42 @@ fn built_in_views_apply_by_name_or_type() {
     assert!(s.execute("perspective.grid.preset", &json!({})).is_err());
 }
 
+#[test]
+fn reapplying_the_current_grid_preset_records_no_undo_step() {
+    let mut s = session();
+    // On a document with no grid defined, a preset defines and shows one: an undo step.
+    run(&mut s, "perspective.grid.preset", json!({"kind": 2}));
+    assert_eq!(undo_len(&s), 1);
+    let g = grid(&s);
+    // The same preset again, by type or by name, leaves the grid as it is: no undo step.
+    run(&mut s, "perspective.grid.preset", json!({"kind": 2}));
+    run(&mut s, "perspective.grid.preset", json!({"name": "[2P-Normal View]"}));
+    assert_eq!((grid(&s), undo_len(&s)), (g.clone(), 1));
+    // Another active plane, or a hidden grid, is set back without an undo step.
+    run(&mut s, "perspective.plane.set", json!({"plane": "ground"}));
+    run(&mut s, "perspective.grid.show", json!({"visible": false}));
+    assert_ne!(grid(&s), g);
+    run(&mut s, "perspective.grid.preset", json!({"kind": 2}));
+    assert_eq!((grid(&s), undo_len(&s)), (g, 1));
+    // Another preset changes the grid.
+    run(&mut s, "perspective.grid.preset", json!({"kind": 3}));
+    assert_eq!((grid(&s).kind, undo_len(&s)), (3, 2));
+}
+
+#[test]
+fn define_grid_with_unchanged_fields_records_no_undo_step() {
+    let mut s = session();
+    // On a document with no grid defined, `perspective.grid.set` stores the grid: an undo step,
+    // and the grid no longer follows the first artboard.
+    run(&mut s, "perspective.grid.set", json!({}));
+    assert_eq!((run(&mut s, "perspective.grid.get", json!({}))["defined"].clone(), undo_len(&s)), (json!(true), 1));
+    // The stored grid's own values leave it as it is: no undo step.
+    let g = grid(&s);
+    run(&mut s, "perspective.grid.set", json!({}));
+    run(&mut s, "perspective.grid.set", json!({"cell": g.cell, "horizon": g.horizon}));
+    assert_eq!((grid(&s), undo_len(&s)), (g, 1));
+}
+
 #[test]
 fn presets_save_rename_delete_and_protect_the_built_in_ones() {
     let mut s = session();
diff --git a/docs/mcp.md b/docs/mcp.md
index 1ad05ba3df..3154b9110b 100644
--- a/docs/mcp.md
+++ b/docs/mcp.md
@@ -10028,8 +10028,10 @@ Perspective grid presets: `perspective.presets.list` lists the built-in views (`
 `[1P-High View]`, `[2P-Normal View]`, `[2P-Low View]`, `[2P-High View]`, `[3P-Normal View]`, `[3P-Low View]`;
 `builtIn: true`, fitted to the first artboard, protected), then the saved ones, each with its Define Grid fields.
 `perspective.grid.preset {name}` (or `{kind}`, that type's normal view) resets the grid to one, fitted to the first
-artboard. `perspective.presets.save {name?, newName?, preset?, …fields}` saves a preset: just `{name}` saves the
-document's grid (View → Perspective Grid → Save Grid as Preset). `perspective.presets.delete {name}`,
+artboard. It adds no undo step when the document already holds that grid. When only whether the grid shows or its
+active plane differs, it sets them without an undo step, as `perspective.grid.show` and `perspective.plane.set` do.
+`perspective.presets.save {name?, newName?, preset?, …fields}` saves a preset: just `{name}` saves the document's grid
+(View → Perspective Grid → Save Grid as Preset). `perspective.presets.delete {name}`,
 `perspective.presets.export {names?, path?}` (a `.vcperspective` JSON file; without `path` it returns `data`) and
 `perspective.presets.import {path? | data? | dataBase64?, replace?}` manage them. Saved presets are kept with the
 preferences, and a grid whose fields are a preset's is named after it (`name`).