I try to avoid these types of sentences all together. It's easy to do.
So instead of.
He looked out the window and saw a little girl...
I write,
He limbed to the window. Outside, a little girl jump roped too close to the street.
It also makes us fill in the blanks, 2+2=4, and we feel a bit smarter for it.
I do a search for filter words: Look, saw, heard, feel, etc
She felt the knife enter her back. Pain shot through her side ...
A two-edged blade punctured her back. Pain exploded as if something broke, something vital.
So I would personally think of other ways to write it. One more example because I find it so easy to use the word "noticed."
He entered the room and noticed a letter on his bed.
At first, I am tempted to rewrite it like this.
He entered the room and spotted a letter on his bed.
Although better, I think it can be improved more.
He entered the room. On his bed, sat a lonely letter, conspicuously staring back at him with a blood stamp sealing its flap.