As a rule of thumb, I would still begin from the wider part of the funnel.

Reason:
if you have a lot of traffic and with that probably a lot of different traffic sources, campaigns, marketing efforts, expectations of the people coming are likely different. Optimization in that case should be done for certain traffic source or visitors segment only. If you manage to get more of those visitors to go down the funnel, you'll get more "juice" to play with and test in the next phase: optimize the next step in the funnel for those visitors/segments only. This would be done much harder (read: slower) if you began from the bottom up.

Regards
Igor