Lemon-Mustard/Pepper-Lime Chicken

I made this recipe by accident once because I thought it was a different recipe, but my husband liked it, so I make it pretty often. Then since I was a little bored of it, I tried one of the recipe variations, and he like that one too. So here are two recipes for the price of one.

2 to 2 1/2 lbs. chicken (I've done just about every kind, bone-in, boneless, whatever)

Lemon-Mustard Glaze:
2 T cooking oil
1 T Dijon-style mustard (I usually use spicy brown)
1 T lemon juice
1 1/2 t lemon pepper
1 t oregano or basil
1/4 t onion salt
1/8 t ground red pepper

OR:
Pepper-Lime Glaze
1/2 t lime peel (I think I left this out because I didn't have any)
1/4 c lime juice
1 T oil
2 cloves minced garlic
1 t coursely ground black pepper
1 t thyme or basil
1/4 t salt

Rinse chicken, pat dry. Broil chicken on a broiler pan about 4-5 inches from heat for 20 minutes or until lightly browned. Stir together the ingredients for one of the above glazes. Brush chicken with glaze, broil for about 5 more minutes. Turn, brush again with glaze, and cook 5-15 more minutes until no longer pink.