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Free-order planning was one depth-first search over parts, contours and entries. A dead end at one part backtracked through every entry combination of the part before it (about 1,450 for a square with two holes) before trying another part order, so a 4 x 4 grid of such parts ran out of its 20000 expansions (and 200000) although cutting it row by row is safe. The whole-part order is now an open travelling-salesman path over part centres from the start point: nearest neighbour, then 2-opt reversals and Or-opt moves of one to three parts, never placing a part before a cutoff or nested-part prerequisite. The existing search then plans contour order and entries along that order. If a part cannot be reached without crossing parts already cut, the search learns "cut it before those", backs up to just before the earliest of them, keeps the parts cut before that point and re-plans the rest from the tool position there. An attempt stops backtracking after 8 x entries x contours expansions without getting further, so it learns instead of retrying the entries of every earlier part. When nothing new can be learned the result is a refusal, as before. A preserved order is planned exactly as before. 16- and 36-part grids, in row order and shuffled, are now ready within the default budget (they were NoSolutionWithinBudget); a 144-part grid plans in about half a second.