Why does union perform better?

I have found that using a UNION to break up a select statement makes it perform much faster (5-10x). The select statement involves inner joins on about 5 tables, and does multiple simple math calculations. The WHERE clause of the first half of the UNION includes selecting 7 of 15 items from a specific table, and the other 8 are selected in the second half. Otherwise, the two parts of the UNION are identical. How can I eliminate the UNION and still maintain the performance? And why is the UNION faster?