How to speed up string construction from characters in a doubly-nested list?

Question

A common speedup for string concatenations is changing something like

s = ""
for x in list:
    s += some_function(x)

to

slist = [some_function(elt) for elt in somelist]
s = "".join(slist)

However, how could this apply if your 'for' was doubly nested? For example...

s = ""
for x in list:
    for y in x:
        s += some_function(y)

Answer 1

''.join(func(c) for s in somelist for c in s)

Answer 2

string_list = []
for x in list:
    for y in x:
        string_list.append(some_function(y))

the_string = ''.join(string_list)