Giving a one week notice

Hey guys i just got offered an amazing new job with a huge salary increase. Problem is this company is known to sometimes pull rug out as far as my research goes. So im waiting on my background check to clear. My current employer however, i feel terrible knowing i will most likely give a one week notice. The new offer i accepted and i start on the first. I know its selfish but i dont want to give my notice until all checks clear. Is it that bad for me to do this? Ive given two weeks notice before but in todays environment i want the utmost security and really want the checks to clear due to my paranoia. Other then burning bridges will i be in a horrible spot if i give one week notice?

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