Hamming Window, python 2.7
In fact Welch was a good idea. End of post. Problem solved.

# Loop for FFT data
for dataset in [fft1]:
    dataset = np.asarray(dataset)
    freqs, psd = welch(dataset, fs=266336/300, window='hamming', nperseg=8192)
    plt.semilogy(freqs, psd/dataset.size**2, color='r')

for dataset2 in [fft2]:
    dataset2 = np.asarray(dataset2)
    freqs2, psd2 = welch(dataset2, fs=266336/300, window='hamming', nperseg=8192)
    plt.semilogy(freqs2, psd2/dataset2.size**2, color='b')