Moving Points at Intersections to Line Segments

[azainomv]

Hi everyone,

I am trying to do a spatial join of traffic incidents along street segments. Some of my points have cross streets as a location, so they show up at intersections. When I do the spatial join, they are double counted for each line segment. 

Is there a way to move the points at intersections to line segments in order to get an accurate join count?

Thank you!

[JohannesBierer]

Don't know how to move the points but would it be an idea to do a intersect instead of spatial join and then use the delete identical tool to remove the double points?