The invention provides a class of oligonucleotide that is optimized to target a specific RNA for RNAse H degradation and to be itself resistant to degradation within in plasma and within eukaryotic, especially mammalian cells. The oligonucleotides of the invention contain no naturally occurring 5'->3'-linked nucleotides. Rather, the invention provides oligonucleotides having two types of nucleotides: 2'-deoxyphosphorothioate, which activate RNase H, and 2'-modified nucleotides, which do not. The linkages between the 2'-modified nucleotides can be phosphodiesters, phosphorothioate or P-ethoxyphosphodiester. Activation of RNAse H is accomplished by a contiguous, RNAse H-activating region, which contains between three and five 2'-deoxyphosphorothioate nucleotides to activate bacterial RNAse H and between five and ten 2'-deoxyphosphorothioate nucleotides to activate eukaryotic and, particularly, mammalian RNAse H. Protection from degradation is accomplished by making the 5' and 3' terminal bases highly nuclease resistant and, optionally, by placing a 3' terminal blocking group.