How to efficiently de-interleave bits (inverse Morton)

This question: How to de-interleave bits (UnMortonizing?) has a good answer for extracting one of the two halves of a Morton number (just the odd bits), but I need a solution which extracts both parts (the odd bits and the even bits) in as few operations as possible.

For my use I would need to take a 32 bit int and extract two 16 bit ints, where one is the even bits and the other is the odd bits shifted right by 1 bit, e.g.

input,  z: 11101101 01010111 11011011 01101110

output, x: 11100001 10110111 // odd bits shifted right by 1
        y: 10111111 11011010 // even bits

There seem to be plenty of solutions using shifts and masks with magic numbers for generating Morton numbers (i.e. interleaving bits), e.g. Interleave bits by Binary Magic Numbers, but I haven't yet found anything for doing the reverse (i.e. de-interleaving).

UPDATE

After re-reading the section from Hacker's Delight on perfect shuffles/unshuffles I found some useful examples which I adapted as follows:

// morton1 - extract even bits

uint32_t morton1(uint32_t x)
{
    x = x & 0x55555555;
    x = (x | (x >> 1)) & 0x33333333;
    x = (x | (x >> 2)) & 0x0F0F0F0F;
    x = (x | (x >> 4)) & 0x00FF00FF;
    x = (x | (x >> 8)) & 0x0000FFFF;
    return x;
}

// morton2 - extract odd and even bits

void morton2(uint32_t *x, uint32_t *y, uint32_t z)
{
    *x = morton1(z);
    *y = morton1(z >> 1);
}

I think this can still be improved on, both in its current scalar form and also by taking advantage of SIMD, so I'm still interested in better solutions (either scalar or SIMD).

If your processor handles 64 bit ints efficiently, you could combine the operations...

int64 w = (z &0xAAAAAAAA)<<31 | (z &0x55555555 )
w = (w | (w >> 1)) & 0x3333333333333333;
w = (w | (w >> 2)) & 0x0F0F0F0F0F0F0F0F; 
...