diff --git a/csi.c b/csi.c
index c755d0af..a199005f 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 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 */
+            /* TODO: don’t need separate cursors */
             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 +525,14 @@ decset_decrst(struct terminal *term, unsigned param, bool enable)
 
             term->grid = &term->normal;
 
+            /* Cursor retains its position from the alt grid */
+            /* TODO: don’t need separate cursors */
             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 +540,7 @@ 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;
@@ -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;
@@ -661,6 +678,8 @@ 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;