Combining Shamir's schemes I am learning about Shamir's secret sharing scheme and I've come across this problem:

Let's suppose we have a combination of a (3, 6) and (1, 2) Shamir's schemes, where participants $P_1$ and $P_2$ get shares in both schemes and others in the first scheme only. The shared secret is the sum of the two shared secrets. Is such a scheme perfect? My guess is that it is, because I can't see how some unprivileged group would learn anything about the secret.
It depends on the access structure.
It is perfect for the structure on $\{P_1, P_2\}$. 
However no subsets of players from $Q=\{P_3,..,P_6\}$ have any information on the secret since they only now one part of the sum.