The online bin covering problem is: given an input sequence of items find a placement of the items in the maximum number of bins such that the sum of the items' sizes in each bin is at least 1. Boyar et al. [3] present a strategy that with O(log log n) bits of advice, where n is the length of the input sequence, achieves a competitive ratio of 8/15 approximate to 0.5333 ... . We show that with a strengthened analysis and some minor improvements, the same strategy achieves the significantly improved competitive ratio of 135/242 approximate to 0.5578 ... , still using O(log log n) bits of advice.