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Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if theresulting 3--manifold K(r) of the surgery has left-orderable fundamental group,and an r-surgery on K is called an L-space surgery if K(r) is an L-space. Aconjecture of Boyer, Gordon and Watson says that non-reducing surgeries on Kcan be classified into left-orderable surgeries or L-space surgeries. Weintroduce a way to provide knots with left-orderable, non-L-space surgeries. Asan application we present infinitely many hyperbolic knots on each of whichevery nontrivial surgery is a hyperbolic, left-orderable, non-L-space surgery.

Left-orderable, non-L-space surgeries on knots