Removing space from header + site title issues

The logo is already close to the top of the page for me, not sure how much closer you are looking to get it. In terms of the tagline, you can try this CSS in Appearance->Customize->Additional CSS

.site-branding .site-description {
	margin-top: -20px;
}

As far as the page title goes, you can try this CSS

#main .page .entry-title {
	display: none;
}

Search engines should still be able to get the title of the page from the <title></title> tags

Thanks for your fast response! I pasted both of those into the Additional CSS box but I’m not seeing results for either. Did I do something wrong?

It removed the header on the normal pages but not on the main page it looks like or at least from what I can guess you’re wanting to do. Instead of

#main .page .entry-title {
	display: none;
}

try

.page .entry-title {
	display: none;
}

In regards to the tagline, you’re referring to the ‘MN orphaned neonatal kitten rescue’ text beneath the logo right?

Right. Basically, I want the header to look like this.

.page didn’t seem to do it either.

Hmm I think this may be what you’re looking for

.site-branding .site-title {
	display: none;
}

That did it, thank you!!