CD74HC4067 analog mux switching times

When I first started using this mux I setup a breadboard and did some tests. I had a bunch of different voltage inputs and switched between them, wired into an analog pin on a Nano, and printing out the read values.

What I found was if I pulled the "E" (enable) pin on the mux high before changing the input address, then pulling it low again, the output would switch cleanly between the different inputs as expected. (The pin is active low so I was basically disabling all output whilst switching address).

If I didn't bother with the E pin and just hot-changed the addresses, then the output seemed to slowly move towards the next voltage over a small period of time, but it was noticeable.

Now I'm wondering if I can free up a pin by getting rid of the line to the E pin. I've looked at the datasheet again and it only mentions a switching time of 6ns, I can't see anything to rationalise the results I previously saw in my experiment.

Before I setup the breadboard and run the tests again, does anyone have any experience with this? Of course, what I want is the quickest and cleanest switch between inputs that I can possibly get.

I don't have any experience with this, and it's hard to tell with no schematic or code, but what comes to mind is a "ripple effect". With the Enable active while the address lines are changing, unless they are being changed simultaneously, the mux output is likely to connect to other inputs, before connecting to the target input, during the process of changing the address.

If so, one solution might be use a "gray code" form of switching, [if applicable] where only one address line need change to get to the next input.

That's a nice idea, thank you. If I setup the breadboard again I'll try an update order that only changes one address one bit at a time.