Does splitting random data reduce its security? Let's say I've got some securely-generated random data I want to encode as words, 32 bits of it.  My wordlist is 2048 words, so each word encodes 11 bits of information.  I write a routine to pack these 32 bits into the lower 11 bits of 3 16-bit types and zero the upper 5 bits of each.  For the last one, I pack in the remaining 10 bits of random data and zero the top 6 instead.  I then look each of these up in my wordlist array to get my words.  I'd like to use these words.

Here's my question: does what I'm doing reduce the amount of secure randomness I'm encoding in these words?  I'd be looking the final word up in a list that's effectively half the size, because the 11th bit is always zero, so is there some "loss of randomness" here?  I know this is a little confusing, but I'd appreciate some guidance.  I suspect there might be some existing guidance on this, but I'm not sure what to search for to find it and none of my googling has yielded results.  

Edit: To clarify, my intuitive guess is that this won't pose a problem, but I'm not comfortable going with that.  The closest I've come to rationalizing this is that $2^{11} \times 2^{11} \times 2^{10} = 2^{32}$.
One way to think about this is that you are defining an encoding, and that this is just a change in representation. You are representing a 32-bit value as 3 words, and importantly this is a reversible process. Since it's a bijective mapping, there's as much entropy in the output as there is in the input.

Really, what you're doing is not fundamentally different from representing the 32-bit value in 9 base 10 digits. It's true that there is notable bias in the leading digit, but the important thing is that the full range is covered and it's invertible.