For general sorting or separating:
* Screen
* Filter
* Sort
* Separate
* Winnow
* Cull
* Pick over
* Examine
For sifting through information:
* Scrutinize
* Analyze
* Investigate
* Study
* Review
* Discern
* Parse
For sifting through memories or thoughts:
* Ruminate
* Contemplate
* Reflect
* Recall
* Recollect
For sifting through a large amount of something:
* Comb through
* Go through
* Search through
* Scan
For sifting something fine:
* Strain
* Sieve
* Mesh
The best alternative will depend on the specific context and what you want to emphasize. For example, "sift through evidence" might be better replaced with "scrutinize evidence," while "sift flour" could be replaced with "strain flour."