2 column between optimization

[Brad Culberson]

I have the following table structure
column a int
column b int

I need to optimize queries similar to the following:
Select * from thattable where a > 1 and a < 2 and b > 3 and b < 5

After making an index including both a and b in ascending order, Explain shows it is not being used...

As a test, I also tried to add index just a and doing the following:
Select * from thattable where a > 1 and a < 2
Explain also shows it is also not being used.

Any ideas would be greatly appreciated.

Thanks,
Brad