The short answers: No, just don't, and severely compromised health.
The long answer: It's important to understand how inbreeding works, at the genetic level, in order to understand the effects. I'm going to assume you have a basic knowledge of Mendelian genetics (heterozygosity, punnet squares, etc) either from bio classes or personal research on herp breeding, and go from there. If this isn't the case, I'm sure we can fix that.
Imagine you have two animals, one of which is het for a rare allele (say a frequency of 1% of the total gene pool), the other has only the normal allele. From basic genetics, we know that there's a 50% (1/2) chance of any given offspring having this allele, and a bit of simple probability shows that there's a 25% (1/4) chance that two randomly selected siblings will both be het for it. Now, if you breed those two offspring together, there's a 25% (1/4) chance any given offspring of the sib-sib mating will be homozygous for that rare allele. So, if we step back and look at the whole picture, if you breed the two parents, randomly pick two sibs and mate them, 1/16th (1/4 * 1/4 = 1/16) of the offspring will be homozygous for the trait that only one parent was het for. In contrast, using the Hardy-Weinberg equations (I can explain these if needed, or point you to approriate websites), at an allele frequency of 1%, only 1 in 10,000 wild snakes would be born homozygous for the rare allele.
Now here's the punchline, and this is very important: Notice that I did not specify what that rare allele was, nor whether it was good or bad. It could be a pretty pattern, or a new beneficial mutation, but it could just as easily be a genetic defect or disease, and therein lies the problem: inbreeding increases homozygosity in a non-selective manner.
Important point number two: What I just described happening for one gene happens for *all* genes in the genome during reproduction (we'll set aside more complex issues such as maternal/paternal biasing and linkage disequilibrium). A good estimate for the genome of a reptile (or just about any vertebrate) is around 20,000 genes, and existing data indicates the average vertebrate (including lizards) is het at about 5% of those loci. A bit of quick math yields 1,000 genes which are present in het state in any given animal, and many of those are damaging mutations.
So what this means is that any given inbred offspring will be homozygous at more loci than normal (which can imprede physiological systems which do best with high genetic diversity, such as the immune system), and this in turn means that it will likely be expressing many negative mutations previously hidden away in het states. The net result is an animal which is weaker, less fit, and a poor competitor compared to it's non-inbred kin, as demonstrated by numerous wild and laboratory experiments.
It's also very hard to weed out these traits: selection on one trait, or a few traits is easy, but 1000? Most of which you can't see? This is actually a limitation of natural selection, called Haldane's paradox, where natural selection can only reasonably act against a few of the many, many genes in a population. After all, what if each of those 1000 have a mere 1% loss of fitness? That's 1000%, and that can't happen: at 100% loss of fitness, you're evolutionarily dead. In a limited population, the more genes natural selection has to act on, the less effectively it acts overall (remember, fitness is always relative, so if *everyone* sucks, there's no selection). Some culling will help, but it cannot alleviate the problem entirely.
Now, as I'm sure you know, brother-sister matings aren't the only form of inbreeding; there's parent-offspring, cousin-cousin, and, in plants and some invertebrates, self-fertilization. Not all forms of inbreeding are equally damaging. Recall the example breeding, and the end probability of a homozygote, 1/16th. Using the same logic, you can evaluate any family tree. Draw a dot for the father or mother (the carrier of the rare allele, doesn't matter which gender). Now, draw a dot for each of the two siblings, and a dot for their offspring. Then, draw an arrow for the gene flow connecting the dots; you should have two arrows from the parent, one to each sib, and an arrow from each sib to the inbred offspring. You should have a total of 4 arrows potentially transmitting the rare allele. Each time, there's a 1/2 chance of transmission, so take 1/2 to the 4th power (multiple 1/2 by 1/2 four times). You should get 1/16th. Now try it for a parent-offspring breeding; you should get an answer of 1/8. Try it for cousins, remembering that, because they're assumed not to carry the rare allele, the outbreeding animals the sibs mate with don't get arrows; the answer should be 1/64. The point is that the more distantly related the breeders are, the lower the intensite of inbreeding, and it decreases very rapidly; by 3rd cousins, there's no detectable effect. This also means that if you do repeated parent-offspring crosses, you'll see problems a lot sooner than if you do sib-sib crosses or cousin-crosses. Which actually brings up my next, and last (I swear!) point:
Inbreeding depression, and the genetic damage that causes it, is accumulative. One round of inbreeding will produce only modest reduction in health and fitness, but each time after that, the reduction will get worse and worse. The intensity of the inbreeding (as above) dictates how long it will take to reach a given loss of health, but even though it takes longer for cousin-cousin inbreeding to show problems, the problems *will* show up eventually.
Anyhow, I hope this wasn't too long and arduous, but I've seen many times where flawed or incomplete genetics knowledge has been used to justify inbreeding. At the end of the day, it's your call: there *will* be some level of health cost to the animals, so it's up to you whether the breeding is worth that.
Henry
