Multiple shipping methods/costs with big range of item sizes

Can someone help me to determine what shipping module would be best for the following situation?

We ship furniture items & accessories, so the package size and item prices have a wide range - for example from a small replacement part which we would ship by DHL/UPS to a sofa or entire patio set which would ship by truck [common carrier] in very large boxes.

We need a shipping module that can look at all the components, possibly by both weight and cubic capacity, to determine what would be the best, and most cost-effective method of shipping.

If this is not possible, we might entertain some kind of averaging method, but our fear is that this will over-price the shipping cost for smaller items and cause loss of sales.

For an idea of our product range, look at http://pipefinepatiofurniture.com and http://patiopads.com.

Any help or suggestions much appreciated.

Terry.