diff --git a/CHANGELOG.md b/CHANGELOG.md
index dcfcb4f4..767f5669 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -36,6 +36,7 @@
   (https://codeberg.org/dnkl/foot/issues/244).
 * Key/mouse binding `select-extend-character-wise`, which forces the
   selection mode to 'character-wise' when extending a selection.
+* `DECSET` `47`, `1047` and `1048`.
 
 
 ### Changed
diff --git a/csi.c b/csi.c
index e833d2a7..9f246a33 100644
--- a/csi.c
+++ b/csi.c
@@ -489,19 +489,31 @@ decset_decrst(struct terminal *term, unsigned param, bool enable)
         break;
 #endif
 
+    case 1048:
+        if (enable)
+            term_save_cursor(term);
+        else
+            term_restore_cursor(term, &term->grid->saved_cursor);
+        break;
+
+    case 47:
+    case 1047:
     case 1049:
         if (enable && term->grid != &term->alt) {
             selection_cancel(term);
 
+            if (param == 1049)
+                term_save_cursor(term);
+
             term->grid = &term->alt;
 
+            /* Cursor retains its position from the normal grid */
             term_cursor_to(
                 term,
-                min(term->grid->cursor.point.row, term->rows - 1),
-                min(term->grid->cursor.point.col, term->cols - 1));
-
-            tll_free(term->alt.scroll_damage);
+                min(term->normal.cursor.point.row, term->rows - 1),
+                min(term->normal.cursor.point.col, term->cols - 1));
 
+            tll_free(term->normal.scroll_damage);
             term_erase(
                 term,
                 &(struct coord){0, 0},
@@ -513,12 +525,13 @@ decset_decrst(struct terminal *term, unsigned param, bool enable)
 
             term->grid = &term->normal;
 
+            /* Cursor retains its position from the alt grid */
             term_cursor_to(
-                term,
-                min(term->grid->cursor.point.row, term->rows - 1),
-                min(term->grid->cursor.point.col, term->cols - 1));
+                term, min(term->alt.cursor.point.row, term->rows - 1),
+                min(term->alt.cursor.point.col, term->cols - 1));
 
-            tll_free(term->alt.scroll_damage);
+            if (param == 1049)
+                term_restore_cursor(term, &term->grid->saved_cursor);
 
             /* Delete all sixel images on the alt screen */
             tll_foreach(term->alt.sixel_images, it) {
@@ -526,6 +539,7 @@ decset_decrst(struct terminal *term, unsigned param, bool enable)
                 tll_remove(term->alt.sixel_images, it);
             }
 
+            tll_free(term->alt.scroll_damage);
             term_damage_all(term);
         }
         break;
@@ -613,6 +627,7 @@ xtsave(struct terminal *term, unsigned param)
     case 12: term->xtsave.cursor_blink = term->cursor_blink.decset; break;
     case 25: term->xtsave.show_cursor = !term->hide_cursor; break;
     case 45: term->xtsave.reverse_wrap = term->reverse_wrap; break;
+    case 47: term->xtsave.alt_screen = term->grid == &term->alt; break;
     case 1000: term->xtsave.mouse_click = term->mouse_tracking == MOUSE_CLICK; break;
     case 1001: break;
     case 1002: term->xtsave.mouse_drag = term->mouse_tracking == MOUSE_DRAG; break;
@@ -626,6 +641,8 @@ xtsave(struct terminal *term, unsigned param)
     case 1035: term->xtsave.num_lock_modifier = term->num_lock_modifier; break;
     case 1036: term->xtsave.meta_esc_prefix = term->meta.esc_prefix; break;
     case 1042: term->xtsave.bell_action_enabled = term->bell_action_enabled; break;
+    case 1047: term->xtsave.alt_screen = term->grid == &term->alt; break;
+    case 1048: term_save_cursor(term); break;
     case 1049: term->xtsave.alt_screen = term->grid == &term->alt; break;
     case 2004: term->xtsave.bracketed_paste = term->bracketed_paste; break;
     case 27127: term->xtsave.modify_escape_key = term->modify_escape_key; break;
@@ -648,6 +665,7 @@ xtrestore(struct terminal *term, unsigned param)
     case 12: enable = term->xtsave.cursor_blink; break;
     case 25: enable = term->xtsave.show_cursor; break;
     case 45: enable = term->xtsave.reverse_wrap; break;
+    case 47: enable = term->xtsave.alt_screen; break;
     case 1000: enable = term->xtsave.mouse_click; break;
     case 1001: return;
     case 1002: enable = term->xtsave.mouse_drag; break;
@@ -661,6 +679,8 @@ xtrestore(struct terminal *term, unsigned param)
     case 1035: enable = term->xtsave.num_lock_modifier; break;
     case 1036: enable = term->xtsave.meta_esc_prefix; break;
     case 1042: enable = term->xtsave.bell_action_enabled; break;
+    case 1047: enable = term->xtsave.alt_screen; break;
+    case 1048: enable = true; break;
     case 1049: enable = term->xtsave.alt_screen; break;
     case 2004: enable = term->xtsave.bracketed_paste; break;
     case 27127: enable = term->xtsave.modify_escape_key; break;
@@ -1141,15 +1161,11 @@ csi_dispatch(struct terminal *term, uint8_t final)
         }
 
         case 's':
-            term->grid->saved_cursor = term->grid->cursor;
-            term->vt.saved_attrs = term->vt.attrs;
-            term->saved_charsets = term->charsets;
+            term_save_cursor(term);
             break;
 
         case 'u':
             term_restore_cursor(term, &term->grid->saved_cursor);
-            term->vt.attrs = term->vt.saved_attrs;
-            term->charsets = term->saved_charsets;
             break;
 
         case 't': {
diff --git a/terminal.c b/terminal.c
index c05325ee..13f7a6f7 100644
--- a/terminal.c
+++ b/terminal.c
@@ -2254,13 +2254,25 @@ term_reset_view(struct terminal *term)
     term_damage_view(term);
 }
 
+void
+term_save_cursor(struct terminal *term)
+{
+    term->grid->saved_cursor = term->grid->cursor;
+    term->vt.saved_attrs = term->vt.attrs;
+    term->saved_charsets = term->charsets;
+}
+
 void
 term_restore_cursor(struct terminal *term, const struct cursor *cursor)
 {
     int row = min(cursor->point.row, term->rows - 1);
     int col = min(cursor->point.col, term->cols - 1);
+
     term_cursor_to(term, row, col);
     term->grid->cursor.lcf = cursor->lcf;
+
+    term->vt.attrs = term->vt.saved_attrs;
+    term->charsets = term->saved_charsets;
 }
 
 void
diff --git a/terminal.h b/terminal.h
index 19fff0e2..04d2d5b7 100644
--- a/terminal.h
+++ b/terminal.h
@@ -106,6 +106,14 @@ struct grid {
     int offset;
     int view;
 
+    /*
+     * Note: the cursor (not the *saved* cursor) could most likely be
+     * global state in the term struct.
+     *
+     * However, we have grid specific functions that does not have
+     * access to the owning term struct, but does need access to the
+     * cursor.
+     */
     struct cursor cursor;
     struct cursor saved_cursor;
 
@@ -595,6 +603,7 @@ void term_reverse_index(struct terminal *term);
 
 void term_arm_blink_timer(struct terminal *term);
 
+void term_save_cursor(struct terminal *term);
 void term_restore_cursor(struct terminal *term, const struct cursor *cursor);
 
 void term_visual_focus_in(struct terminal *term);
diff --git a/vt.c b/vt.c
index bbb7e990..b932c716 100644
--- a/vt.c
+++ b/vt.c
@@ -378,15 +378,11 @@ action_esc_dispatch(struct terminal *term, uint8_t final)
     case 0:
         switch (final) {
         case '7':
-            term->grid->saved_cursor = term->grid->cursor;
-            term->vt.saved_attrs = term->vt.attrs;
-            term->saved_charsets = term->charsets;
+            term_save_cursor(term);
             break;
 
         case '8':
             term_restore_cursor(term, &term->grid->saved_cursor);
-            term->vt.attrs = term->vt.saved_attrs;
-            term->charsets = term->saved_charsets;
             break;
 
         case 'c':