Speaker relative efficiency/sensitivity when using a high pass filter

200 W “peak unclipped program”

I have a Minidsp on order to use as a digital crossover, my Audio Physic Sitara 25 speakers are ported (89db / 36 Hz specification). I use with stereo subwoofers and Vincent SA31MK / SP331MK amplification.  I want to reduce the load on the power amp and speakers as the Vincent is class A for the first 10 watts. (Not sure if that means into 8 ohms ? as AP's are 4 ohm load then could be 10 watts or maybe 20 watts?). I will be experimenting and will add my experiences to this page.

@tcutter , if you take the bass out of a speaker with any high pass filter you increase the headroom of the amplifier driving the speaker but you do not change the efficiency of the speaker one iota, it remains exactly the same. Depending on where the crossover is in the speaker you may lower distortion at some frequencies. With a full range loudspeaker this can make a very noticeable reduction in distortion at moderate to high volumes certainly over 80 dB.

Understood, hence my calling it "relative efficiency".  I appreciate that your and Erik's replies are semantically more appropriate.

So it appears there is a decrement in the current/voltage required to drive a speaker to only 80Hz instead of 35 or so. I am wondering if there is a formula to determine what the quantity might be. My impetus is that requiring less power allows me to consider lower power amps, perhaps even making Class A available.