Dealing with a strong ordering effect


I'm conducting a study in which people have to judge a perceptual effect (by rating it on a 10 point continous scale). I have three levels of this effect and there are two different contexts. There was a first study in which the order of the effects was randomized, but not the contexts. So participants first were with each effect within the first context and then in the second context. Giving all in all 6 ratings (each effect level in each context). But there is a huge effect visible for the worst condition coming from the ordering in both contexts. If a person was presented with the worst effect in the first round of the context his or her rating would be in average more than one sd higher compared to when the effect was presented in the third (last) round.
I don't have the resources to scale up the number of participants (I think the first study had 24 - I'm aiming for a similar number).

Is there a good statistical way to approach this ordering? The problem that I see is that it is not only an effect of in which round the effect was presented, but in which order. E.g. participants which were presented with the medium level effect rated it better when presented before with the worse effect compared to when presented before with the best level.

So I am wondering now if it would be beneficial to go for two orderings (good to bad and bad to good). Then I would be able to say something about what happens if you get this effect depending on which effect you had before.

Anybody have experience in dealing with studies have a strong ordering effect or knows some good read on the topic?

Thank you