How to plot the lines first and points last in matplotlib

I have a simple plot with several sets of points and lines connecting each set. I want the points to be plotted on top of the lines (so that the line doesn't show inside the point). Regardless of order of the plot and scatter calls, this plot comes out the same, and not as I'd like. Is there a simple way to do it?

import math
import matplotlib.pyplot as plt

def poisson(m):
    def f(k):
        e = math.e**(-m)
        f = math.factorial(k)
        g = m**k
        return g*e/f
    return f

R = range(20)
L = list()
means = (1,4,10)
for m in means:
    f = poisson(m)
    L.append([f(k) for k in R])
colors = ['r','b','purple']

for c,P in zip(colors,L):
    plt.plot(R,P,color='0.2',lw=1.5)
    plt.scatter(R,P,s=150,color=c)
    
ax = plt.axes()
ax.set_xlim(-0.5,20)
ax.set_ylim(-0.01,0.4)
plt.savefig('example.png')

You need to set the Z-order.

plt.plot(R,P,color='0.2',lw=1.5, zorder=1)
plt.scatter(R,P,s=150,color=c, zorder=2)

Check out this example. http://matplotlib.sourceforge.net/examples/pylab_examples/zorder_demo.html