SumIf only if value is above a certain number

I have used SumIf to determine add numbers using the regular criteria, for example:
=sumif($A1:$A6,$A1:$A6,$B1:$B6) to return the sums of values in B that match the row criteria in A many times with great success.

Now I need to do something more complicated. I only want to sum the value in B if it is over a specific number, like 10. I have tried nesting an IF statement and it doesn't look like that is the way to go.

Thanks in advance for your help,

micheldun