powerbook,
In that case just ignore CL (unless you are trading it) and focus on the instrument you are trading.
Except for a sample of days, the stock market has actually been just as reactive to news events related (directly or indirectly) to oil and to pundits' articles on threats to supply, etc as it has been to actual CL price changes.
Rule of thumb: By the time a new 'correlate' becomes obvious / known - its real influence is already on the wane... ie milk it, but don't expect it to be a golden teet...
hth
zdo