There are a number of specialized data structures that implement ordered dictionaries for integer keys: van Emde Boas trees, y-Fast tries, fusion trees, etc. Each of these data structures implement the key ordered dictionary primitives in sublogarithmic time.
However, to the best of my knowledge, all three of the above data structures are interesting only in a theoretical context, since their hidden constant factors are so large that they're effectively impractical. (I may be wrong about that, though!)
Are there any integer data structures that support sublogarithmic query times in theory which are also efficient in practice?