Second mitten, how to prevent gap near thumb?

[haapai]

There's a pretty big gap at the base of the thumb on my first mitten (actually a fingerless mitt) and I don't want the same to show up in my second mitt (ever).  Do any of you know any tricks or techniques for avoiding such gaps.  Would picking up more stitches than the pattern specifies do some of the trick?  Or is the secret to knit as tightly as possible. 

I suspect that I could google the question and receive lots of possible answers but I don't know how to analyze the answers that I find.  I think that googling it would lead to to adopting the first or easiest solution that I find and that one might not be the best. 

The base of my thumbs may be unusually wide.  This is the free pattern that I am using. 

Any tips?