Custom Command for Subitem with Itemize

Question

I found following code from the comments on Possible to create bullets for \subitems using \itemize without a nested list?

\newcommand{\cvSubItem}[1]{%
    {\setlength\itemindent{15pt} \item[{\includegraphics[width=0.3cm]{bullet.png}}] #1}
}

Two problems:

1. The first letter of the SubItems has space to the others. It looks like: "s pace" instead of "space".

2. If the line breaks, it should start at the same point as the text, not as the bullet:

* this happens
if the line breaks

* this should happen
  if the line breaks

!!!UPDATE!!!

I also tried this code for the nested variant:

\newlist{SubItemList}{itemize}{1}
\setlist[SubItemList]{label={$-$}}
\let\OldItem\item
\newcommand{\SubItemStart}[1]{%
    \let\item\SubItemEnd
    \begin{SubItemList}[resume]%
        \OldItem #1%
}
\newcommand{\SubItemMiddle}[1]{%
    \OldItem #1%
}
\newcommand{\SubItemEnd}[1]{%
    \end{SubItemList}%
    \let\item\OldItem
    \item #1%
}
\newcommand*{\cvSubItem}[1]{%
    \let\cvSubItem\SubItemMiddle%
    \SubItemStart{#1}%
}%

This works well for the first Subitems. But if I have following list:

\item
\cvSubItem
\cvSubitem
\item
\cvSubItem
\cvSubItem

It only works for the first part.

Thanks for help!