There are a few ways to make a break 'convincing'. Subtleties can usually be broken down into three categories: before, during, and after.
Before - as tiggerkim mentioned, there is no substitute for good structuring of an effect to draw attention away from the deck when you need to hold a break. Proper use of misdirection combined with good routining is the MOST important factor in making a break deceptive. John Carney, a student of Vernon and one of the giants of our time, would say that misdirection is everything, technique is just insurance in case misdirection fails.
The skill to do this will increase as you get more exposure in magic. Watch some of the greats perform - especially Tommy Wonder and Johny Carney, both of which exemplifies the principles of misdirection. David Williamson is also a good example. Watch not just for their effects, but look for why they do/say certain things, WHEN do they do a sleight, what happens before that? what happens after? and so on and so forth
For written resources on the structuring of routine and misdirection, check out Tommy Wonder's Books of Wonder, there's a massive 50 page section of theory on misdirection. John Carney's Book of Secrets. Daniel Fitzgee's Magic by Misdirection and Auturo de Ascanio's The Magic of Ascanio volume 1.
During - There is a simple fix to reduce the visible gap at the front of the gap - use a smaller break! Simple concept, but actually quite hard to do in practice. Charlie Miller used to advocate the use of an extremely small break. A smaller break may be more deceptive, but it is harder to handle, but there's an interesting technique of Vernon's in the Vernon Chronicles Vol. 1 under "To enlarge a break" that has nullified this problem for me - always hold a small break, and when a technique needs to be performed, use the Vernon technique to enlarge the break. Briefly: if you're holding a small break with your left pinky, the right hand comes over and grips the deck in a biddle grip. The right thumb exerts a slight pressure on the rear of the deck as the right hand squares the ends of the deck. Under the proper pressures, the break will enlarge with each right to left passing of the thumb in the squaring action, enlarge until desired size is reached.
A slight forward bevel of the deck or a messy square up of the top half will also help conceal a break.
After - There are several subtleties or displays that you can do while holding a break to convince the spectators that it is not possible to hold a break. Here are some (not a comprehensive list).
Two solutions of Charlie Miller's are to rotate the left and and riffle the end of the non-break side with the right thumb, and to tap the end of the deck on the table using both hands (Both published in Harry Riser's excellent Secrets of an Escamoteur). You can use both hands to simply squeeze the deck to bow it along its length in a concave and convex manner while holding a break (a Max Malini subtlety), use the right hand to riffle the left length of the deck held vertically on its right side back into the left palm (a move of Earnest Earick's published in By Forces Unseen), or my favorite sequence, remove the left thumb and balance the deck on just your left fingers (A technique of Roger Klause's in Roger Klause in Concert).
And of course, combined with a jog, the possibilities become endless.
Hope this helps! Let me know if you have any more questions.