  Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the
resulting 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. A
conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K
can be classified into left-orderable surgeries or L-space surgeries. We
introduce a way to provide knots with left-orderable, non-L-space surgeries. As
an application we present infinitely many hyperbolic knots on each of which
every nontrivial surgery is a hyperbolic, left-orderable, non-L-space surgery.
