Remove 1 qty of product Magento - ajax

Question

I'm implementing custom sidebar cart of Magento, which will feature incrementation and decrementaton of products in this cart, refreshed in ajax.
AJAX is possible to work just with HTML, isn't working as return value is whole cart.
I'm adding 1 quantity of product using CartController: /checkout/cart/add/uenc/aHR0cDovL3BsYXkudGhlaGFwcHlwZWFyLm5ldC9zaG9wL2RyaW5rcw,,/product/586/
Is it possible to just remove 1 quantity of product? Do I have to create new custom function in CartController?
Thanks,
Adam
ANSWER:
you can call this link with
/checkout/cart/remove/id/ $ITEMID /uenc/aHR0cDovL3BsYXkudGhlaGFwcHlwZWFyLm5ldC9zaG9w/ (depending on your magento settings link could be different)
Copy into CartController.php
public function removeAction()
{
$cart = $this->_getCart();
$params = $this->getRequest()->getParams();
try {
if (isset($params['qty'])) {
$filter = new Zend_Filter_LocalizedToNormalized(
array('locale' => Mage::app()->getLocale()->getLocaleCode())
);
$params['qty'] = $filter->filter($params['qty']);
}
$product = $this->_initProduct();
$related = $this->getRequest()->getParam('related_product');
/**
* Check product availability
*/
$id = (int) $this->getRequest()->getParam('id');
$items = $cart->getItems();
foreach ($items as $item) {
if ($item->getProduct()->getId() == $id) {
if( $item->getQty() == 1 ){
$cart->removeItem($item->getItemId())->save();
}
else if($item->getQty() > 1){
$item->setQty($item->getQty() - 1);
$cart->save();
}
break;
}
}
$this->_getSession()->setCartWasUpdated(true);
/**
* #todo remove wishlist observer processAddToCart
*/
Mage::dispatchEvent('checkout_cart_add_product_complete',
array('product' => $product, 'request' => $this->getRequest(), 'response' => $this->getResponse())
);
if (!$this->_getSession()->getNoCartRedirect(true)) {
if (!$cart->getQuote()->getHasError()){
//$message = $this->__('%s was added to your shopping cart.', Mage::helper('core')->escapeHtml($product->getName()));
//$this->_getSession()->addSuccess($message);
}
$this->_goBack();
}
} catch (Mage_Core_Exception $e) {
if ($this->_getSession()->getUseNotice(true)) {
$this->_getSession()->addNotice(Mage::helper('core')->escapeHtml($e->getMessage()));
} else {
$messages = array_unique(explode("\n", $e->getMessage()));
foreach ($messages as $message) {
$this->_getSession()->addError(Mage::helper('core')->escapeHtml($message));
}
}
$url = $this->_getSession()->getRedirectUrl(true);
if ($url) {
$this->getResponse()->setRedirect($url);
} else {
$this->_redirectReferer(Mage::helper('checkout/cart')->getCartUrl());
}
} catch (Exception $e) {
$this->_getSession()->addException($e, $this->__('Cannot add the item to shopping cart.'));
Mage::logException($e);
$this->_goBack();
}
}