In some situations, we might expect that context effects will massively affect preferences. For example, if we are working out how to price a completely new product, we can be confident that if we price it at $5 and $10 in the experiment, we will find preference at $10 to be substantially lower. But, it may be that if we had just shown it at $10, the preference measured at $10 would have been the same as if we had just priced it at $5.
The fix for such context effects is to use split cell designs. A design is first created as if the problem does not exist by excluding the problematic attribute (or merging levels). Half the respondents see the questions created from this design with the price at $5. The other half see the same design, but at $10 for the new product.