Building Git with HTTPS support: avoiding libcurl?

I'm trying to build Git (2.6.4) on GNU/Linux, but without any requirements (other than basic libc etc.) on the local system. This works fine except for one thing: git-remote-https.

In order to build this I need to have libcurl, but libcurl is a MONSTER library with an enormous number of prerequisites (see below).

Just wondering if anyone has considered an alternative to libcurl; maybe I'm wrong but it seems to me that HTTPS support for Git would require only a tiny fraction of the libcurl features and maybe there's an alternative available which would be more targeted?

I realize this is not a short-term thing in that there won't be an API compatible library that can just be dropped in. This is more a forward -looking question. For now I'm looking to see if I can rebuild libcurl myself without most of these dependencies such as Kerberos, LDAP, etc.

$ ldd /usr/lib/x86_64-linux-gnu/libcurl.so.4
        linux-vdso.so.1 =>  (0x00007fff37d81000)
        libidn.so.11 => /usr/lib/x86_64-linux-gnu/libidn.so.11 (0x00007f682b921000)
        librtmp.so.1 => /usr/lib/x86_64-linux-gnu/librtmp.so.1 (0x00007f682b704000)
        libssl.so.1.0.0 => /lib/x86_64-linux-gnu/libssl.so.1.0.0 (0x00007f682b49a000)
        libcrypto.so.1.0.0 => /lib/x86_64-linux-gnu/libcrypto.so.1.0.0 (0x00007f682b058000)
        libgssapi_krb5.so.2 => /usr/lib/x86_64-linux-gnu/libgssapi_krb5.so.2 (0x00007f682ae0e000)
        liblber-2.4.so.2 => /usr/lib/x86_64-linux-gnu/liblber-2.4.so.2 (0x00007f682abfe000)
        libldap_r-2.4.so.2 => /usr/lib/x86_64-linux-gnu/libldap_r-2.4.so.2 (0x00007f682a9ac000)
        libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007f682a792000)
        libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f682a573000)
        libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f682a1a9000)
        libgnutls-deb0.so.28 => /usr/lib/x86_64-linux-gnu/libgnutls-deb0.so.28 (0x00007f6829e8d000)
        libhogweed.so.4 => /usr/lib/x86_64-linux-gnu/libhogweed.so.4 (0x00007f6829c59000)
        libnettle.so.6 => /usr/lib/x86_64-linux-gnu/libnettle.so.6 (0x00007f6829a23000)
        libgmp.so.10 => /usr/lib/x86_64-linux-gnu/libgmp.so.10 (0x00007f68297a3000)
        libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007f682959e000)
        libkrb5.so.3 => /usr/lib/x86_64-linux-gnu/libkrb5.so.3 (0x00007f68292cc000)
        libk5crypto.so.3 => /usr/lib/x86_64-linux-gnu/libk5crypto.so.3 (0x00007f682909d000)
        libcom_err.so.2 => /lib/x86_64-linux-gnu/libcom_err.so.2 (0x00007f6828e98000)
        libkrb5support.so.0 => /usr/lib/x86_64-linux-gnu/libkrb5support.so.0 (0x00007f6828c8d000)
        libresolv.so.2 => /lib/x86_64-linux-gnu/libresolv.so.2 (0x00007f6828a71000)
        libsasl2.so.2 => /usr/lib/x86_64-linux-gnu/libsasl2.so.2 (0x00007f6828855000)
        libgssapi.so.3 => /usr/lib/x86_64-linux-gnu/libgssapi.so.3 (0x00007f6828615000)
        /lib64/ld-linux-x86-64.so.2 (0x0000559b03259000)
        libp11-kit.so.0 => /usr/lib/x86_64-linux-gnu/libp11-kit.so.0 (0x00007f68283b0000)
        libtasn1.so.6 => /usr/lib/x86_64-linux-gnu/libtasn1.so.6 (0x00007f682819c000)
        libkeyutils.so.1 => /lib/x86_64-linux-gnu/libkeyutils.so.1 (0x00007f6827f98000)
        libheimntlm.so.0 => /usr/lib/x86_64-linux-gnu/libheimntlm.so.0 (0x00007f6827d8e000)
        libkrb5.so.26 => /usr/lib/x86_64-linux-gnu/libkrb5.so.26 (0x00007f6827b04000)
        libasn1.so.8 => /usr/lib/x86_64-linux-gnu/libasn1.so.8 (0x00007f6827861000)
        libhcrypto.so.4 => /usr/lib/x86_64-linux-gnu/libhcrypto.so.4 (0x00007f682762d000)
        libroken.so.18 => /usr/lib/x86_64-linux-gnu/libroken.so.18 (0x00007f6827418000)
        libffi.so.6 => /usr/lib/x86_64-linux-gnu/libffi.so.6 (0x00007f6827210000)
        libwind.so.0 => /usr/lib/x86_64-linux-gnu/libwind.so.0 (0x00007f6826fe6000)
        libheimbase.so.1 => /usr/lib/x86_64-linux-gnu/libheimbase.so.1 (0x00007f6826dd7000)
        libhx509.so.5 => /usr/lib/x86_64-linux-gnu/libhx509.so.5 (0x00007f6826b8c000)
        libsqlite3.so.0 => /usr/lib/x86_64-linux-gnu/libsqlite3.so.0 (0x00007f68268be000)
        libcrypt.so.1 => /lib/x86_64-linux-gnu/libcrypt.so.1 (0x00007f6826686000)