  A recent breakthrough in the theory of (type A) Macdonald polynomials is due
to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these
polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram
and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms
of so-called alcove walks; these originate in the work of Gaussent-Littelmann
and of the author with Postnikov on discrete counterparts to the Littelmann
path model. In this paper, we relate the above developments, by explaining how
the Ram-Yip formula compresses to a new formula, which is similar to the
Haglund-Haiman-Loehr one but contains considerably fewer terms.
