I use a sieve, but that is personal preference. I don't think it is possible to get every little bit out. What I like about veggies stock is no fat and it's not as messy to make as turkey stock with the bones fat, and veggies.
I always make a big batch, so I have to strain it in batches and then let it sit for a bit b/c there is alot of stock liquid in those veggies and bones. I sometimes push it down... amazing how much liquid squeezes through.
I make more effort to strain the turkey stock b/c I want as much fat out of it as possible. After I strain the bones and veggies out, I put the pot in the fridge or garage to chill so the fat will settle on top. The next day, I skim off all the fat and strain again with a sieve to ensure little bones are out.