diff --git a/src/g_demo.cpp b/src/g_demo.cpp
index 9ea033f53..405163790 100644
--- a/src/g_demo.cpp
+++ b/src/g_demo.cpp
@@ -1548,8 +1548,9 @@ skippedghosttic:
 		if (*g->p == DEMOMARKER)
 		{
 			g->mo->momx = g->mo->momy = g->mo->momz = 0;
-#if 1 // freeze frame (maybe more useful for time attackers)
+#if 0 // freeze frame (maybe more useful for time attackers) (2024-03-11: you leave it behind anyway!)
 			g->mo->colorized = true;
+			g->mo->fuse = 10*TICRATE;
 			if (follow)
 				follow->colorized = true;
 #else // dissapearing act
diff --git a/src/k_hud.cpp b/src/k_hud.cpp
index d5d16ab49..9d80582f6 100644
--- a/src/k_hud.cpp
+++ b/src/k_hud.cpp
@@ -4425,27 +4425,28 @@ static void K_drawKartMinimap(void)
 		demoghost *g = ghosts;
 		while (g)
 		{
-			if (g->mo->skin)
-				skin = ((skin_t*)g->mo->skin)-skins;
-			else
-				skin = 0;
-
-			workingPic = R_CanShowSkinInDemo(skin) ? faceprefix[skin][FACE_MINIMAP] : kp_unknownminimap;
-
-			if (g->mo->color)
+			if (g->mo && !P_MobjWasRemoved(g->mo) && g->mo->skin)
 			{
-				if (g->mo->colorized)
-					colormap = R_GetTranslationColormap(TC_RAINBOW, static_cast<skincolornum_t>(g->mo->color), GTC_CACHE);
+				skin = ((skin_t*)g->mo->skin)-skins;
+
+				workingPic = R_CanShowSkinInDemo(skin) ? faceprefix[skin][FACE_MINIMAP] : kp_unknownminimap;
+
+				if (g->mo->color)
+				{
+					if (g->mo->colorized)
+						colormap = R_GetTranslationColormap(TC_RAINBOW, static_cast<skincolornum_t>(g->mo->color), GTC_CACHE);
+					else
+						colormap = R_GetTranslationColormap(skin, static_cast<skincolornum_t>(g->mo->color), GTC_CACHE);
+				}
 				else
-					colormap = R_GetTranslationColormap(skin, static_cast<skincolornum_t>(g->mo->color), GTC_CACHE);
+					colormap = NULL;
+
+				interpx = R_InterpolateFixed(g->mo->old_x, g->mo->x);
+				interpy = R_InterpolateFixed(g->mo->old_y, g->mo->y);
+
+				K_drawKartMinimapIcon(interpx, interpy, x, y, splitflags, workingPic, colormap);
 			}
-			else
-				colormap = NULL;
 
-			interpx = R_InterpolateFixed(g->mo->old_x, g->mo->x);
-			interpy = R_InterpolateFixed(g->mo->old_y, g->mo->y);
-
-			K_drawKartMinimapIcon(interpx, interpy, x, y, splitflags, workingPic, colormap);
 			g = g->next;
 		}
 	}
diff --git a/src/k_respawn.c b/src/k_respawn.c
index 6bb98db0e..d2da452db 100644
--- a/src/k_respawn.c
+++ b/src/k_respawn.c
@@ -509,6 +509,13 @@ static void K_MovePlayerToRespawnPoint(player_t *player)
 				player->respawn.distanceleft = 0;
 			}
 
+			// Almost all legitimate driving, no matter how clumsy, should be faster than death in TA.
+			// Advance only as far as we need to prevent respawn loops!
+			if (modeattacking)
+			{
+				player->respawn.distanceleft = 0;
+			}
+
 			player->respawn.wp = player->respawn.wp->nextwaypoints[nwp];
 			K_RespawnAtWaypoint(player, player->respawn.wp);
 
diff --git a/src/p_inter.c b/src/p_inter.c
index fa3652788..b586c7481 100644
--- a/src/p_inter.c
+++ b/src/p_inter.c
@@ -2571,7 +2571,7 @@ static boolean P_KillPlayer(player_t *player, mobj_t *inflictor, mobj_t *source,
 			return false;
 		}
 
-		if (modeattacking)
+		if (modeattacking & ATTACKING_SPB)
 		{
 			// Death in SPB Attack is an instant loss.
 			P_DoPlayerExit(player, PF_NOCONTEST);