I tried sieving mine years ago but found it too time consuming although the consistency was good. Over the years I have tried/burnt out many blenders juicers and I find a really good high rpm food blender (not a stick blender unless your doing small amounts) makes a really good base sauce.

We make vast quantities of Base sauce at the Uni and we ALWAYS pass this through a conical strainer. It makes for a far better result at the end.

I've never had to strain my base if you have a decent blender either hand held or a fixed one you should
be able to get a smooth consistency.