We present a deterministic O(log n log log n) space algorithm for
undirected s,t-connectivity. It is based on the deterministic EREW
algorithm of Chong and Lam (SODA 93) and uses the universal
exploration sequences for trees constructed by Kouck\'y (CCC 01).
Our result improves the O(log^{4/3} n) bound of Armoni et al.
(STOC 97) and is a big step towards the optimal O(log n).
Independently of our result and using a different set of techniques,
the optimal bound was achieved recently by Reingold (ECCC TR04-94).