diff --git a/src/Curl/Curl.jl b/src/Curl/Curl.jl
index e4f5171..7167ade 100644
--- a/src/Curl/Curl.jl
+++ b/src/Curl/Curl.jl
@@ -29,10 +29,6 @@ using LibCURL
 using LibCURL: curl_off_t
 # not exported: https://github.com/JuliaWeb/LibCURL.jl/issues/87
 
-# constants that LibCURL should have but doesn't
-const CURLE_PEER_FAILED_VERIFICATION = 60
-const CURLSSLOPT_REVOKE_BEST_EFFORT = 1 << 3
-
 using NetworkOptions
 using Base: preserve_handle, unpreserve_handle
 
@@ -68,8 +64,14 @@ function with_handle(f, handle::Union{Multi, Easy})
 end
 
 setopt(easy::Easy, option::Integer, value) =
-    @check curl_easy_setopt(easy.handle, option, value)
+    @check curl_easy_setopt(easy.handle, CURLoption(option), value)
 setopt(multi::Multi, option::Integer, value) =
-    @check curl_multi_setopt(multi.handle, option, value)
+    @check curl_multi_setopt(multi.handle, CURLMoption(option), value)
+
+# CEnum is no longer Integer in LibCURL.jl
+setopt(easy::Easy, option::CURLoption, value) = setopt(easy, Int(option), value)
+setopt(multi::Multi, option::CURLMoption, value) = setopt(multi, Int(option), value)
+Base.zero(::CURLcode) = CURLE_OK
+Base.zero(::CURLMcode) = CURLM_OK
 
 end # module
diff --git a/src/Downloads.jl b/src/Downloads.jl
index 5e07a74..8f245d4 100644
--- a/src/Downloads.jl
+++ b/src/Downloads.jl
@@ -230,7 +230,7 @@ function download(
             downloader = downloader,
         )
         status_ok(response.proto, response.status) && return output
-        throw(RequestError(url, Curl.CURLE_OK, "", response))
+        throw(RequestError(url, Int(Curl.CURLE_OK), "", response))
     end
 end
 
@@ -365,7 +365,7 @@ function request(
                 response = Response(get_response_info(easy)...)
                 easy.code == Curl.CURLE_OK && return response
                 message = get_curl_errstr(easy)
-                response = RequestError(url, easy.code, message, response)
+                response = RequestError(url, Int(easy.code), message, response)
                 throw && Base.throw(response)
             end
         end
diff --git a/test/runtests.jl b/test/runtests.jl
index fd4bb20..363beed 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -275,7 +275,7 @@ include("setup.jl")
 
         err = @exception download("$server/status/404")
         @test err isa RequestError
-        @test err.code == 0 && isempty(err.message)
+        @test err.code == Int(Curl.CURLE_OK) && isempty(err.message)
         @test err.response.status == 404
         @test contains(err.response.message, r"^HTTP/\d+(?:\.\d+)?\s+404\b")
         @test err.response.proto === "https"
@@ -414,7 +414,7 @@ include("setup.jl")
         @testset "bad TLS is rejected" for url in urls
             resp = request(url, throw=false)
             @test resp isa RequestError
-            @test resp.code == Curl.CURLE_PEER_FAILED_VERIFICATION
+            @test resp.code == Int(Curl.CURLE_PEER_FAILED_VERIFICATION)
         end
         @testset "easy hook work-around" begin
             local url