I used to get into the most horrendous tangles before I started working this way.
Added on March 1st:
OK, let's not write up any more laudatory reviews of Lara Croft, guys. It goes right to her head.
Look at this post. What was I thinking? Like, did I invent this technique? No. In the state of self-exaltation you guys left me in, I omitted to mention that I learned it from another blog. Whose blog? Why, whose do you think? Carol Ventura's blog, of course! To see where I learned this choreography, go to this page. My crocheting life is divided into a Before and After Carol's page on Tapestry Crochet in Finland!
IMPORTANT: WORKED IN ROUNDS!
1. Let's call red A and white B. Hold A in the normal manner, and B flat over the top of the work.
4. Now change colours. Pass the hook behind A....
6. and pull B through, completing the stitch.
7. Now insert hook in Back Loop of next stitch,
and pick up B from where it's lying over top of the work.
I find that if I have to do a longer stretch (more than 3 sts) of colour B, it's more graceful to drop both strands and pick them up again with their positions reversed. The strand you hold in the normal manner is faster for most of us to work.
Doggy is optional but happy.