My Google-fu Is Weak

So I'm taking an oil painting class and we're painting plants. No problem, I like plants. However, this week, my plant is an orchid. (So pretty.) The problem I'm having is that the petals are a really pretty pale yellow/tan run through with darker yellow/tan and purple. We aren't allowed to use any white paint for this painting. No problem, I thought. I thinned out a blend of lemon hue and cadmium yellow with a little alizarin crimson and let the white gesso show through.

However, my professor wants my flowers to have a thicker, more opaque look. (My background is a pthalo blue blend where I'm trying to show the light and while I'm using thin layer, I admit the flowers look bizarrely washed out against my background.) However, I have no idea how to do this without white. To my knowledge, the only ways to thin the pigment/make it paler are adding white or thinning out with a medium. I'm already a little concerned that some of the flowers on the side are too intensely orange when the real life flowers are a delicate and pale color (if you go here, the petals are like beige and cream).

I know there are artist types on my flist. Help?