How to efficiently generate random tests in Haskell Test.QuickCheck

I'd like to generate some sample tests using Haskell Test.QuickCheck

The goal is to generate data of (Int, [Int]) with the following conditions where the tuple is (x, xs):

1. x > 0
2. x not in xs
3. all xs >0

Scratching my head and stumbling through the manual http://ift.tt/2m4pjDK after some time I can produce random lists meeting these requirements:

import Test.QuickCheck
mygen = arbitrary::Gen (Int, [Int]))
sample (mygen `suchThat` ( \(x, xs)->( (x `notElem` xs) && (x > 0) && (all (>0) xs)&& (xs/=[]))))

Running the last line in the GHCI outputs something like:

(40,[19,35,27,29,45,1,17,28])
(20,[3,9,11,12,15,8])
(43,[76,102,106,71,24,2,29,101,59,48])
(99,[5,87,136,131,22,22,133])
(77,[11,14,55,47,78,15,14])
...

Questions:

1. How can this be done more efficiently since - I'm guessing- the function mygen creates a large sample set then filters out based on the suchThat criteria

2. How can I indicate the list xs should be of a certain size. For example if I add && length xs > 50 the program runs for a very long time.

3. Guarantee that each element of xs is unique. I.e. avoid records like (99,[22,22])