Hello,
In addition to what Lars stated, I'd check if all your joins are using appropriate cardinality.
By the looks of your model I'd set left outer from data foundation to dimension CVs and if the cardinality is set correctly the optimization process that runs before execution could remove unwanted joins.
I believe that would work by default from SP09 on... at least that's what my test shows. Here's a snapshot of my test model and result for LOV query:
BRs,
Lucas de Oliveira