(ALP + DNAase I) may help 

we use Qiagen RNeasy kit for purification of TB RNA. It has gDNA eliminator column. after purification we give DNase treatment using kit ambion DNase kit. RNA comes out very pure. Good luck.

selective precipitation of RNA from mixture using lithium chloride works ,refer sambrook (provided if you like to use manual method).

If your RNA sample has either organic or protein contamination DNase might not work. Also, during collection of aqueous phase don't be greedy to collect all the supernatant. Don't overload TRIzol with cells.

thank you...