Erasing with Putty?
This is not a putty rubber as you know it...  Be prepared to have your technical illusions shattered - my preferred eraser (almost my only eraser) is not an eraser at all... but it is a tool of unsurpassed excellence!  We know it here in the UK as "Blu-Tack" - the non-sticky putty that is used for fixing posters to walls.  Yes, that's right, this stuff is God's own gift to graphite artists - and probably works as well with charcoal and pastel.  Years ago I bought a batch of putty rubbers (kneaded erasers) that broke up in use and, in desperation, I grabbed a piece of Blu-Tack — I've used virtually nothing else since.  This "eraser" is so versatile that I still haven't exhausted its range of uses!  But beware - there are similar products, generically known as "Wall Putties", but only Blu-Tack possesses the qualities we need.

The Eraser in use:   Blu-Tack possesses two qualities not found in Putty Rubbers - an enhanced ability to be readily formed into any shape and an all-important inherent tackiness.  And one undesirable but not insurmountable property - it's tendency to become soft and sticky when held in the hand for any length of time.  This is easily overcome by employing two balls of the magic putty so that one is always cool and available for immediate use.

An Eraser is not a Rubber:   Hard rubbers rub, they do little more than force graphite deep into the paper.  "Art erasers" and putty types remove graphite more softly but, as they still require a dragging movement to achieve results, a degree of graphite "staining" usually results.  But Blu-Tack, as a result of its sticky nature, removes every grain of graphite without any detrimental movement.  It's a graphite magnet!  A quick downward touch embeds the grains for immediate and clean lifting.

Cleaning the Eraser:   In time, as the Blu-Tack eraser takes in more and more graphite, it will cease to be as efficient.  However most of the graphite is merely embedded in its surface and just requires dilution by distributing it throughout the eraser.  Taking the ball of putty in one hand, simply pull off small pieces or stretch it out into a long length - now roll the whole thing up again and knead it back into a ball.  This eraser is a miser's dream... it will last for months!

Lightening tone:   Never again will you feel afraid of over-darkening an area of your drawing.  The day has arrived when you can load an area with as much graphite as you want because you now have the means to remove it if you need to.  The following technique can be applied to any area of tone that you require to be a little (or a lot) lighter.  This is where rubbers are useless and normal erasers will let you down - neither can remove half a layer of graphite without disturbing the remainder beneath.  This Eraser can!  Roll the putty into a cylinder with as smooth a face as possible (try rolling it on your drawing board).  Now gently roll the cylinder over the area to be lightened and repeat as required.  With a little practice you will soon become proficient and will be able to lower a complete area from in-your-face to ghostly!... and without affecting the detail!  For small areas just rock your eraser on your drawing board to form a curved flat then rock that in turn on your drawing.  This technique allows total control over the subtlety of, for example, a misty scene - draw it with ease using a greater strength and a wider range of contrasts than is required then use your eraser to progressively "fade" as required.

Complete Erasure:   Try this out for yourself and follow the steps I took below:
1:  Take a piece of your usual drawing paper (I prefer Ivorex card) and generously apply a saturated coating of 6B or similar to a small area.  A harder grade will do but it has to be one that you know a regular eraser will smear and not remove.
2:  Roll a cylinder of your Blu-Tack eraser over the area.  This will remove all the surface graphite.
3:  Continue rolling until the eraser (which you might need to clean at some stage)...
4:  has removed as much graphite as it possibly can.  The graphite is removed in ever decreasing amounts so persevere.  Don't worry that the coated eraser may deposit graphite back onto your paper - it just doesn't happen!
5:  Remember when I said the eraser "removes every grain of graphite...and embeds the grains for immediate and clean lifting"?  Well, that's in an ideal world — the very act of drawing will have pushed some graphite a little too far into the paper for the putty to reach so now (and only now) reach for your soft art eraser and rub out the final remnants.