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The traditional channel routing problem is known to be solvable, if and only if the constraint graph is acyclic. In the letter we examine channels with two-terminal nets without doglegging and assume that some terminals are interchangeable. A necessary and sufficient condition is established for the interchangeability of the points to ensure solvability. Regular channel structures, like those in gate arrays, are compared. The routability condition is shown to be weaker if noninter-changeable points have different abscissas.