Accessibility and Search Engine Optimization (SEO)

Hi All--
I've run into contradictory opinions about SEO optimization and accessibility best practices for images.
My understanding: 
   
   - Title tags for images are unnecessary and increase clutter unless 1) an alternative description cannot be provided for an image (can't think of an example), in which case a screen reader will default to the title, or 2) they provide information that is contained in an alternative description but not available--and would be helpful--to sighted users.
   - Having alternative text for an image when it is described by adjacent text is redundant to screen reader users and should be avoided.

SEO Expert opinion:   
   - Every image should have both an alternative description and a title to optimize SEO.
   - Adjacent text is important to SEO, so include it as well.   


Can anyone sort this out? I've found a couple of articles that say image titles have a minimal affect, but nothing that addresses this directly.
Thanks...
Mike