Improve subplot size/spacing with many subplots

I need to generate a whole bunch of vertically-stacked plots in matplotlib. The result will be saved using savefig and viewed on a webpage, so I don't care how tall the final image is, as long as the subplots are spaced so they don't overlap.

No matter how big I allow the figure to be, the subplots always seem to overlap.

My code currently looks like

import matplotlib.pyplot as plt
import my_other_module

titles, x_lists, y_lists = my_other_module.get_data()

fig = plt.figure(figsize=(10,60))
for i, y_list in enumerate(y_lists):
    plt.subplot(len(titles), 1, i)
    plt.xlabel("Some X label")
    plt.ylabel("Some Y label")
    plt.title(titles[i])
    plt.plot(x_lists[i],y_list)
fig.savefig('out.png', dpi=100)

Please review matplotlib: Tight Layout guide and try using matplotlib.pyplot.tight_layout, or matplotlib.figure.Figure.tight_layout

As a quick example:

import matplotlib.pyplot as plt

fig, axes = plt.subplots(nrows=4, ncols=4, figsize=(8, 8))
fig.tight_layout() # Or equivalently,  "plt.tight_layout()"

plt.show()

Without Tight Layout

With Tight Layout