  In this paper, we give an efficient algorithm of degree reduction of B\'ezier
curves with box constraints. The idea is to combine the previous iterative
approach, that has been presented recently in (P. Gospodarczyk, Comput. Aided
Des. 62 (2015), 143--151), with a fast method of construction of dual bases
from (P. Wo\'zny, J. Comput. Appl. Math. 260 (2014), 301--311) and a new
efficient method of modification of dual bases.
