diff --git a/INSTALL b/INSTALL
index 66389ce059..4140a3f5c8 100644
--- a/INSTALL
+++ b/INSTALL
@@ -138,12 +138,15 @@ Issues of note:
 	  BLK_SHA1.  Also included is a version optimized for PowerPC
 	  (PPC_SHA1).
 
-	- "libcurl" library is used by git-http-fetch, git-fetch, and, if
-	  the curl version >= 7.34.0, for git-imap-send.  You might also
-	  want the "curl" executable for debugging purposes. If you do not
-	  use http:// or https:// repositories, and do not want to put
-	  patches into an IMAP mailbox, you do not have to have them
-	  (use NO_CURL).
+	- "libcurl" library is used for fetching and pushing
+	  repositories over http:// or https://, as well as by
+	  git-imap-send if the curl version is >= 7.34.0. If you do
+	  not need that functionality, use NO_CURL to build without
+	  it.
+
+	  Git requires version "7.19.4" or later of "libcurl" to build
+	  without NO_CURL. This version requirement may be bumped in
+	  the future.
 
 	- "expat" library; git-http-push uses it for remote lock
 	  management over DAV.  Similar to "curl" above, this is optional
diff --git a/Makefile b/Makefile
index 9df565f27b..a9f9b689f0 100644
--- a/Makefile
+++ b/Makefile
@@ -1421,15 +1421,8 @@ else
 	REMOTE_CURL_NAMES = $(REMOTE_CURL_PRIMARY) $(REMOTE_CURL_ALIASES)
 	PROGRAM_OBJS += http-fetch.o
 	PROGRAMS += $(REMOTE_CURL_NAMES)
-	curl_check := $(shell (echo 070908; $(CURL_CONFIG) --vernum | sed -e '/^70[BC]/s/^/0/') 2>/dev/null | sort -r | sed -ne 2p)
-	ifeq "$(curl_check)" "070908"
-		ifndef NO_EXPAT
-			PROGRAM_OBJS += http-push.o
-		else
-			EXCLUDED_PROGRAMS += git-http-push
-		endif
-	else
-		EXCLUDED_PROGRAMS += git-http-push
+	ifndef NO_EXPAT
+		PROGRAM_OBJS += http-push.o
 	endif
 	curl_check := $(shell (echo 072200; $(CURL_CONFIG) --vernum | sed -e '/^70[BC]/s/^/0/') 2>/dev/null | sort -r | sed -ne 2p)
 	ifeq "$(curl_check)" "072200"
diff --git a/git-curl-compat.h b/git-curl-compat.h
new file mode 100644
index 0000000000..a308bdb3b9
--- /dev/null
+++ b/git-curl-compat.h
@@ -0,0 +1,128 @@
+#ifndef GIT_CURL_COMPAT_H
+#define GIT_CURL_COMPAT_H
+#include <curl/curl.h>
+
+/**
+ * This header centralizes the declaration of our libcurl dependencies
+ * to make it easy to discover the oldest versions we support, and to
+ * inform decisions about removing support for older libcurl in the
+ * future.
+ *
+ * The oldest supported version of curl is documented in the "INSTALL"
+ * document.
+ *
+ * The source of truth for what versions have which symbols is
+ * https://github.com/curl/curl/blob/master/docs/libcurl/symbols-in-versions;
+ * the release dates are taken from curl.git (at
+ * https://github.com/curl/curl/).
+ *
+ * For each X symbol we need from curl we define our own
+ * GIT_CURL_HAVE_X. If multiple similar symbols with the same prefix
+ * were defined in the same version we pick one and check for that name.
+ *
+ * We may also define a missing CURL_* symbol to its known value, if
+ * doing so is sufficient to add support for it to older versions that
+ * don't have it.
+ *
+ * Keep any symbols in date order of when their support was
+ * introduced, oldest first, in the official version of cURL library.
+ */
+
+/**
+ * CURL_SOCKOPT_OK was added in 7.21.5, released in April 2011.
+ */
+#if LIBCURL_VERSION_NUM < 0x071505
+#define CURL_SOCKOPT_OK 0
+#endif
+
+/**
+ * CURLOPT_TCP_KEEPALIVE was added in 7.25.0, released in March 2012.
+ */
+#if LIBCURL_VERSION_NUM >= 0x071900
+#define GITCURL_HAVE_CURLOPT_TCP_KEEPALIVE 1
+#endif
+
+
+/**
+ * CURLOPT_LOGIN_OPTIONS was added in 7.34.0, released in December
+ * 2013.
+ *
+ * If we start requiring 7.34.0 we might also be able to remove the
+ * code conditional on USE_CURL_FOR_IMAP_SEND in imap-send.c, see
+ * 1e16b255b95 (git-imap-send: use libcurl for implementation,
+ * 2014-11-09) and the check it added for "072200" in the Makefile.
+
+ */
+#if LIBCURL_VERSION_NUM >= 0x072200
+#define GIT_CURL_HAVE_CURLOPT_LOGIN_OPTIONS 1
+#endif
+
+/**
+ * CURL_SSLVERSION_TLSv1_[012] was added in 7.34.0, released in
+ * December 2013.
+ */
+#if LIBCURL_VERSION_NUM >= 0x072200
+#define GIT_CURL_HAVE_CURL_SSLVERSION_TLSv1_0
+#endif
+
+/**
+ * CURLOPT_PINNEDPUBLICKEY was added in 7.39.0, released in November
+ * 2014.
+ */
+#if LIBCURL_VERSION_NUM >= 0x072c00
+#define GIT_CURL_HAVE_CURLOPT_PINNEDPUBLICKEY 1
+#endif
+
+/**
+ * CURL_HTTP_VERSION_2 was added in 7.43.0, released in June 2015.
+ *
+ * The CURL_HTTP_VERSION_2 alias (but not CURL_HTTP_VERSION_2_0) has
+ * always been a macro, not an enum field (checked on curl version
+ * 7.78.0)
+ */
+#if LIBCURL_VERSION_NUM >= 0x072b00
+#define GIT_CURL_HAVE_CURL_HTTP_VERSION_2 1
+#endif
+
+/**
+ * CURLSSLOPT_NO_REVOKE was added in 7.44.0, released in August 2015.
+ *
+ * The CURLSSLOPT_NO_REVOKE is, has always been a macro, not an enum
+ * field (checked on curl version 7.78.0)
+ */
+#if LIBCURL_VERSION_NUM >= 0x072c00
+#define GIT_CURL_HAVE_CURLSSLOPT_NO_REVOKE 1
+#endif
+
+/**
+ * CURLOPT_PROXY_CAINFO was added in 7.52.0, released in August 2017.
+ */
+#if LIBCURL_VERSION_NUM >= 0x073400
+#define GIT_CURL_HAVE_CURLOPT_PROXY_CAINFO 1
+#endif
+
+/**
+ * CURLOPT_PROXY_{KEYPASSWD,SSLCERT,SSLKEY} was added in 7.52.0,
+ * released in August 2017.
+ */
+#if LIBCURL_VERSION_NUM >= 0x073400
+#define GIT_CURL_HAVE_CURLOPT_PROXY_KEYPASSWD 1
+#endif
+
+/**
+ * CURL_SSLVERSION_TLSv1_3 was added in 7.53.0, released in February
+ * 2017.
+ */
+#if LIBCURL_VERSION_NUM >= 0x073400
+#define GIT_CURL_HAVE_CURL_SSLVERSION_TLSv1_3 1
+#endif
+
+/**
+ * CURLSSLSET_{NO_BACKENDS,OK,TOO_LATE,UNKNOWN_BACKEND} were added in
+ * 7.56.0, released in September 2017.
+ */
+#if LIBCURL_VERSION_NUM >= 0x073800
+#define GIT_CURL_HAVE_CURLSSLSET_NO_BACKENDS
+#endif
+
+#endif
diff --git a/http.c b/http.c
index a0f169d2fe..d7c20493d7 100644
--- a/http.c
+++ b/http.c
@@ -1,4 +1,5 @@
 #include "git-compat-util.h"
+#include "git-curl-compat.h"
 #include "http.h"
 #include "config.h"
 #include "pack.h"
@@ -47,19 +48,19 @@ static struct {
 	{ "sslv2", CURL_SSLVERSION_SSLv2 },
 	{ "sslv3", CURL_SSLVERSION_SSLv3 },
 	{ "tlsv1", CURL_SSLVERSION_TLSv1 },
-#if LIBCURL_VERSION_NUM >= 0x072200
+#ifdef GIT_CURL_HAVE_CURL_SSLVERSION_TLSv1_0
 	{ "tlsv1.0", CURL_SSLVERSION_TLSv1_0 },
 	{ "tlsv1.1", CURL_SSLVERSION_TLSv1_1 },
 	{ "tlsv1.2", CURL_SSLVERSION_TLSv1_2 },
 #endif
-#if LIBCURL_VERSION_NUM >= 0x073400
+#ifdef GIT_CURL_HAVE_CURL_SSLVERSION_TLSv1_3
 	{ "tlsv1.3", CURL_SSLVERSION_TLSv1_3 },
 #endif
 };
 static const char *ssl_key;
 static const char *ssl_capath;
 static const char *curl_no_proxy;
-#if LIBCURL_VERSION_NUM >= 0x072c00
+#ifdef GIT_CURL_HAVE_CURLOPT_PINNEDPUBLICKEY
 static const char *ssl_pinnedkey;
 #endif
 static const char *ssl_cainfo;
@@ -373,10 +374,10 @@ static int http_options(const char *var, const char *value, void *cb)
 	}
 
 	if (!strcmp("http.pinnedpubkey", var)) {
-#if LIBCURL_VERSION_NUM >= 0x072c00
+#ifdef GIT_CURL_HAVE_CURLOPT_PINNEDPUBLICKEY
 		return git_config_pathname(&ssl_pinnedkey, var, value);
 #else
-		warning(_("Public key pinning not supported with cURL < 7.44.0"));
+		warning(_("Public key pinning not supported with cURL < 7.39.0"));
 		return 0;
 #endif
 	}
@@ -500,7 +501,7 @@ static int has_cert_password(void)
 	return 1;
 }
 
-#if LIBCURL_VERSION_NUM >= 0x073400
+#ifdef GIT_CURL_HAVE_CURLOPT_PROXY_KEYPASSWD
 static int has_proxy_cert_password(void)
 {
 	if (http_proxy_ssl_cert == NULL || proxy_ssl_cert_password_required != 1)
@@ -516,7 +517,7 @@ static int has_proxy_cert_password(void)
 }
 #endif
 
-#if LIBCURL_VERSION_NUM >= 0x071900
+#ifdef GITCURL_HAVE_CURLOPT_TCP_KEEPALIVE
 static void set_curl_keepalive(CURL *c)
 {
 	curl_easy_setopt(c, CURLOPT_TCP_KEEPALIVE, 1);
@@ -536,7 +537,7 @@ static int sockopt_callback(void *client, curl_socket_t fd, curlsocktype type)
 	if (rc < 0)
 		warning_errno("unable to set SO_KEEPALIVE on socket");
 
-	return 0; /* CURL_SOCKOPT_OK only exists since curl 7.21.5 */
+	return CURL_SOCKOPT_OK;
 }
 
 static void set_curl_keepalive(CURL *c)
@@ -732,7 +733,7 @@ static long get_curl_allowed_protocols(int from_user)
 	return allowed_protocols;
 }
 
-#if LIBCURL_VERSION_NUM >=0x072f00
+#ifdef GIT_CURL_HAVE_CURL_HTTP_VERSION_2
 static int get_curl_http_version_opt(const char *version_string, long *opt)
 {
 	int i;
@@ -774,7 +775,7 @@ static CURL *get_curl_handle(void)
 		curl_easy_setopt(result, CURLOPT_SSL_VERIFYHOST, 2);
 	}
 
-#if LIBCURL_VERSION_NUM >= 0x072f00 // 7.47.0
+#ifdef GIT_CURL_HAVE_CURL_HTTP_VERSION_2
     if (curl_http_version) {
 		long opt;
 		if (!get_curl_http_version_opt(curl_http_version, &opt)) {
@@ -805,7 +806,7 @@ static CURL *get_curl_handle(void)
 
 	if (http_ssl_backend && !strcmp("schannel", http_ssl_backend) &&
 	    !http_schannel_check_revoke) {
-#if LIBCURL_VERSION_NUM >= 0x072c00
+#ifdef GIT_CURL_HAVE_CURLSSLOPT_NO_REVOKE
 		curl_easy_setopt(result, CURLOPT_SSL_OPTIONS, CURLSSLOPT_NO_REVOKE);
 #else
 		warning(_("CURLSSLOPT_NO_REVOKE not supported with cURL < 7.44.0"));
@@ -845,20 +846,20 @@ static CURL *get_curl_handle(void)
 		curl_easy_setopt(result, CURLOPT_SSLKEY, ssl_key);
 	if (ssl_capath != NULL)
 		curl_easy_setopt(result, CURLOPT_CAPATH, ssl_capath);
-#if LIBCURL_VERSION_NUM >= 0x072c00
+#ifdef GIT_CURL_HAVE_CURLOPT_PINNEDPUBLICKEY
 	if (ssl_pinnedkey != NULL)
 		curl_easy_setopt(result, CURLOPT_PINNEDPUBLICKEY, ssl_pinnedkey);
 #endif
 	if (http_ssl_backend && !strcmp("schannel", http_ssl_backend) &&
 	    !http_schannel_use_ssl_cainfo) {
 		curl_easy_setopt(result, CURLOPT_CAINFO, NULL);
-#if LIBCURL_VERSION_NUM >= 0x073400
+#ifdef GIT_CURL_HAVE_CURLOPT_PROXY_CAINFO
 		curl_easy_setopt(result, CURLOPT_PROXY_CAINFO, NULL);
 #endif
 	} else if (ssl_cainfo != NULL || http_proxy_ssl_ca_info != NULL) {
 		if (ssl_cainfo != NULL)
 			curl_easy_setopt(result, CURLOPT_CAINFO, ssl_cainfo);
-#if LIBCURL_VERSION_NUM >= 0x073400
+#ifdef GIT_CURL_HAVE_CURLOPT_PROXY_CAINFO
 		if (http_proxy_ssl_ca_info != NULL)
 			curl_easy_setopt(result, CURLOPT_PROXY_CAINFO, http_proxy_ssl_ca_info);
 #endif
@@ -927,7 +928,6 @@ static CURL *get_curl_handle(void)
 		 */
 		curl_easy_setopt(result, CURLOPT_PROXY, "");
 	} else if (curl_http_proxy) {
-#if LIBCURL_VERSION_NUM >= 0x071800
 		if (starts_with(curl_http_proxy, "socks5h"))
 			curl_easy_setopt(result,
 				CURLOPT_PROXYTYPE, CURLPROXY_SOCKS5_HOSTNAME);
@@ -940,8 +940,7 @@ static CURL *get_curl_handle(void)
 		else if (starts_with(curl_http_proxy, "socks"))
 			curl_easy_setopt(result,
 				CURLOPT_PROXYTYPE, CURLPROXY_SOCKS4);
-#endif
-#if LIBCURL_VERSION_NUM >= 0x073400
+#ifdef GIT_CURL_HAVE_CURLOPT_PROXY_KEYPASSWD
 		else if (starts_with(curl_http_proxy, "https")) {
 			curl_easy_setopt(result, CURLOPT_PROXYTYPE, CURLPROXY_HTTPS);
 
@@ -1006,7 +1005,7 @@ void http_init(struct remote *remote, const char *url, int proactive_auth)
 	free(normalized_url);
 	string_list_clear(&config.vars, 1);
 
-#if LIBCURL_VERSION_NUM >= 0x073800
+#ifdef GIT_CURL_HAVE_CURLSSLSET_NO_BACKENDS
 	if (http_ssl_backend) {
 		const curl_ssl_backend **backends;
 		struct strbuf buf = STRBUF_INIT;
diff --git a/imap-send.c b/imap-send.c
index 49a5f8aa59..e6090a0346 100644
--- a/imap-send.c
+++ b/imap-send.c
@@ -1441,7 +1441,7 @@ static CURL *setup_curl(struct imap_server_conf *srvc, struct credential *cred)
 	curl_easy_setopt(curl, CURLOPT_PORT, server.port);
 
 	if (server.auth_method) {
-#if LIBCURL_VERSION_NUM < 0x072200
+#ifndef GIT_CURL_HAVE_CURLOPT_LOGIN_OPTIONS
 		warning("No LOGIN_OPTIONS support in this cURL version");
 #else
 		struct strbuf auth = STRBUF_INIT;