Kelly makes an excellent suggestion.
The other option is to use an intermdiate needle --- maybe instead of going directly from a 3 to a 13, you knit one row on the 3, one on a 7 and the next on the 13. That way you won't have to fight to get those big 'ol 13's through a size 3 hole (not an easy task), but instead you get your 13's through a size 7 hole.
I would think you'd get the same net effect as knitting loosely the row before you switch to 13s. but this way you'll be more consistent with the size of your stitches on the row before.
Hope that helps!