Why is css-nano (almost) not working?

Question

gulp-minify-css says its deprecated, and points to gulp-css-nano as its successor.

How come, I reach so much weaker results with cssnano?

I do the minifything (and beautify afterwards for readability):

gulp.task('teststyles-nano', [], function () {
    gulp.src('css/testcase.css')
    .pipe( nano() )
    .pipe( cssbeautify() )
    .pipe( rename('nano.css' ))
    .pipe( gulp.dest('./public/') );
});

gulp.task('teststyles-minify', [], function () {
    gulp.src('css/testcase.css')
    .pipe( minifyCss() )   // resp.  .pipe(minifyCss())
    .pipe( cssbeautify() )
    .pipe( rename('minify.css') )  // resp.  'minify.css'
    .pipe( gulp.dest('./public/') );
});

Here's my testcase.css, with plenty of intentional stuff to optimize:

html, body {
    margin: 0;
    padding: 0;
}

h1, h2, h3 {
    color: green;
    color: purple;  /* redundant in place */
    background-color: #caa;
}
html, body {  /* combine to above, remove duplicates? */
    margin: 0;   
    background-color: #aac;
}

/* group media queries,
   remove redundant rules and/or combine p, div */
@media only screen and (max-width: 500px) {
    p { background-color: orange; }
}
@media only screen and (max-width: 500px) {
    p { background-color: purple; }
    div { background-color: purple; }
}

h1, h2, h3, h1, h2 { /* combine to above, remove double selectors */
    font-family: 'Helvetica Neue', Helvetica, Arial, Arial, Arial, sans-serif;
    font-weight: bold;
    color: orange;
    text-decoration: underline;

    margin-top: 10px;  /* screams combining */
    margin-right: 20px;
    margin-bottom: 10px;
    margin-left: 20px;
}

minify.css has pretty much all expected, where nano.css simply does not:

I am under Windows7, x64. Versions:

npm list --depth=0 | grep -i css
├── css-purge@1.1.1 extraneous
├── gulp-css-purge@1.0.27
├── gulp-cssbeautify@0.1.3
├── gulp-cssnano@2.1.1
├── gulp-minify-css@1.2.3

Thus I am pretty clueless, on such an isolated case.

Answer 1

I got feedback from the plugin author: These optimizations are not yet implemented.

That means, it's not about wrong parameters or use, which was basically my question. He recommends gulp-clean-css as an alternative.

I think I will stick with gulp-minify-css for a little while longer.