Using Hirasawa–Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on $S^3$. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.
Kenneth L. BAKER. Allison H. MOORE. "Montesinos knots, Hopf plumbings, and L-space surgeries." J. Math. Soc. Japan 70 (1) 95 - 110, January, 2018. https://doi.org/10.2969/jmsj/07017484