The exponential growth of the number of test conditions (i.e., the “run size”) of a 2k factorial design makes the design prohibitively expensive for a large k. When only m of the 2k effects/interactions are non-zero, only m test conditions are required for their estimation. However, both fractional factorial design and Taguchi method require 2n test conditions, for some n ⩽ k, and therefore may require more test conditions than necessary. Given the identities of the m non-zero effects/interactions, Tsao and Wibowo recently developed an algorithm to identify a set of exactly m test conditions but did not suggest how to test the adequacy of the m-unknown model or how to expand the set of test conditions incrementally when more non-zero effects/interactions actually exist. This paper proposes to incrementally and efficiently expand the model by developing an effect–interaction sequence in the descending order of their magnitudes. Given any such sequence, we provide a simple algorithm to sequence the 2k test conditions so that, for any m, 1 ⩽ m ⩽ 2k, the first m effects/interactions in the effect–interaction sequence can be estimated with exactly the first m test conditions in the corresponding test-condition sequence and no more, if all the other 2k − m effects/interactions are zero. A benefit of this is that experiments can be performed sequentially according to the test-condition sequence until the first insignificant effect/interaction is found. The proposed method can also be used for situations where knowledge about the effects/interactions is too vague to sort them according to their magnitudes.