Which expression host are you using? To get tight control with IPTG induction, you need also the lac repressor (lacI) either in the host genome or on a plasmid. To my knowledge, pQE30 does not produce the lac repressor, and some frequently used expression strains such as BL21 do not provide genomic lacI, therefore are OK for non-toxic proteins, but leaky expression is deleterious for toxic products.

Sorry for chiming in so late but this migh be useful for someone else.

Annemarie Honegger, BL21 does produce the lacI repressor (see e.g. https://www.genome.jp/dbget-bin/www_bget?ebl:ECD_00299). The reason why expression plasmids carrying hybrid T7/lac promoters carry their own lacI copy is to avoid titrating out the cellular repressor due to the increased number of lac operator sites.

Tang Zhi Zhuang, yes, there may be induction without IPTG for any of a number of reasons. Reason number one is titration of existing LacI tetramers as explained above; you should ensure that the strain used carries a copy of the LacIq allele (which expresses LacI at higher levels) either in the chromosome or in the plasmid itself. This especially critical with pQE30; see Article Facile promoter deletion in Escherichia coli in response to ...

Another reason is the presence of trace amounts of lactose in the peptone/tryptone used to prepare culture media; this was the problem that prompted the development of autoinduction media by Studier. Obviously for this to be a problem the strain must have a functional copy of the lactose permease (lacY).

Remember that the T5 promoter of the pQE vector family is simply another sigma-70 conventional promoter with lac operators thrown in for regulation and has nothing to do with those of the T7 family, which depend on their own RNA polymerase.

Hope it helps!