Fair's Fair

Can you design a die which rolls 'fairly' against mine?
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Problem



This table shows the possible outcomes when two normal dice (my dice and your dice) are rolled and their scores added together.

You can use the table to see that the probability of getting a sum of $2$ is $\frac1{36}$, the probability of getting a sum of $3$ is $\frac2{36}$ and so on.



              My dice
Your dice    1   2   3  4 5 6
 1  2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

Imagine that I change my dice slightly by replacing the 2 with an 8.

Can you choose numbers for the faces of your dice so that the two dice still perform in exactly the same way when thrown as a pair (ie so that the probability of getting a sum of $2$ is still $\frac1{36}$, the probability of getting a sum of $3$ is still $\frac2{36}$, and so on)?