» T7 Express Iq (NEB #C3014): over-expression of the LacI repressor reduces basal expression of the T7 RNA polymerase
» T7 Express lysY (NEB #C3010): lysY produces mutant T7 lysozyme which binds to T7 RNA polymerase, reducing basal expression of the target protein. Upon induction, newly made T7 RNA polymerase titrates out the lysozyme and results in expression of the target protein
» T7 Express Iq/lysY (NEB #C3013) combines both above effects.
Incubation at 30°C or room temperature may also alleviate toxicity issues. In addition, check antibiotic concentration (test with control plasmid).