Can you identify the poem beginning I heard thy death with scarce a sigh?

This may be a misquotation of the first two lines in Lord Byron's "Stanzas on the Death of the Duke of Dorset".

Or not.

Anyway, Byron's work begins:

"I heard thy fate without a tear,

Thy loss with scarce a sigh;

And yet thou wert surpassing dear -

Too loved of all to die.

I know not what hath seared mine eye,

The tears refuse to start;

But every drop its lids deny

Falls dreary on my heart."