1. Use a minimalist design approach. Especially with contemporary pieces, you can easily simplify a frame design to ,minimize its impact in a room. For canvasses, float frames may be a good option. When you are forces to use a narrow mat border due to lack of wall space, it will probably look better to float the art over the mat using 1/2″ border versus cutting a window in a mat with a 1″ border.
2. For art on paper, try switching from a wider moulding to a narrower cap profile. This can buy you the space you need for the mat border width you want.