Maybe one of your compounds is an aggregator. You could check out http://advisor.bkslab.org/ to get an idea and also for recommandations how to perform appropriate control experiments. Typically they include: addition of detergent, change protein concentration and check for specificity. Also other false positive mechanisms are possible like reactivity etc. - here you could use the PAINS filter or look up your compounds at http://pasilla.health.unm.edu/tomcat/badapple/badapple to get an idea about potential promiscuity. 

If you can rule out false positive behavior, a potential allosteric mechanism could play a role as you have two binding sites. This of course has to be proven carefully. 

Please clarify whether you mean the association constant (Ka) increased (the second inhibitor bound more tightly in the presence of the first), or the dissociation constant (Kd) increased (the second inhibitor bound less tightly in the presence of the first.

If the Ka increased, you are probably seeing a positively cooperative interaction between the to ligand binding sites. If the Kd increased, you may be seeing negative cooperativity between the two sites, or the two inhibitors may be competing for the binding sites. Or it may be an artifact, such as those mentioned by Jonas Aretz, or a fluorescence artifact (e.g. inner filter effect).