diff --git a/gnu/packages/cmake.scm b/gnu/packages/cmake.scm
index 135863f6c2..806a7396e9 100644
--- a/gnu/packages/cmake.scm
+++ b/gnu/packages/cmake.scm
@@ -51,7 +51,7 @@ (define-module (gnu packages cmake)
 (define-public cmake-minimal
   (package
     (name "cmake-minimal")
-    (version "3.15.1")
+    (version "3.16.0")
     (source (origin
               (method url-fetch)
               (uri (string-append "https://www.cmake.org/files/v"
@@ -59,7 +59,7 @@ (define-public cmake-minimal
                                   "/cmake-" version ".tar.gz"))
               (sha256
                (base32
-                "1xyprly3sf4wi0n1x79k4n22yxm6pb7fv70gqr9lvc7qv14cbphq"))
+                "0pwcgvk75577rdizpzjrk2n43a6l7rvfhmhn7sd6xarwqrb6b9bd"))
               (modules '((guix build utils)))
               (snippet
                '(begin
@@ -101,6 +101,8 @@ (define-public cmake-minimal
        (let ((skipped-tests
               (list "BundleUtilities" ; This test fails on Guix.
                     "CTestTestSubdir" ; This test fails to build 2 of the 3 tests.
+                    ;; This test requires 'ldconfig' which is not available in Guix.
+                    "RunCMake.install"
                     ;; These tests requires network access.
                     "CTestCoverageCollectGCOV"
                     "CTestTestUpload")))
@@ -125,7 +127,7 @@ (define-public cmake-minimal
              ;; files.
              (substitute*
                  '("Modules/CompilerId/Xcode-3.pbxproj.in"
-                   "Modules/CPack.RuntimeScript.in"
+                   "Modules/Internal/CPack/CPack.RuntimeScript.in"
                    "Source/cmGlobalXCodeGenerator.cxx"
                    "Source/cmLocalUnixMakefileGenerator3.cxx"
                    "Source/cmExecProgramCommand.cxx"
@@ -218,22 +220,6 @@ (define-public cmake-minimal-cross
     (search-paths
      (package-native-search-paths cmake-minimal))))
 
-(define-public cmake-3.15.5
-  ;; CMake 3.15.5 fixes some issues, but declare another version to
-  ;; avoid triggering the rebuild of all CMake-based packages.
-  ;; See <https://issues.guix.gnu.org/issue/38060>.
-  (package
-    (inherit cmake)
-    (version "3.15.5")
-    (source (origin
-              (inherit (package-source cmake))
-              (uri (string-append "https://www.cmake.org/files/v"
-                                  (version-major+minor version)
-                                  "/cmake-" version ".tar.gz"))
-              (sha256
-               (base32
-                "1d5y8d92axcc6rfqlsxamayfs3fc1vdby91hn5mx1kn02ppprpgv"))))))
-
 (define-public emacs-cmake-mode
   (package
     (inherit cmake)
diff --git a/gnu/packages/patches/cmake-curl-certificates.patch b/gnu/packages/patches/cmake-curl-certificates.patch
index 36252083f8..7fe2615271 100644
--- a/gnu/packages/patches/cmake-curl-certificates.patch
+++ b/gnu/packages/patches/cmake-curl-certificates.patch
@@ -6,19 +6,19 @@ as well as /etc/ssl/certs.
 
 --- cmake-3.13.1/Source/cmCurl.cxx	2019-09-10 17:27:36.926907260 +0200
 +++ cmake-3.13.1/Source/cmCurl.cxx	2019-09-10 17:52:35.475903919 +0200
-@@ -4,11 +4,8 @@
- 
- #include "cmThirdParty.h"
+@@ -2,11 +2,8 @@
+    file Copyright.txt or https://cmake.org/licensing for details.  */
+ #include "cmCurl.h"
  
 -#if !defined(CMAKE_USE_SYSTEM_CURL) && !defined(_WIN32) &&                    \
 -  !defined(__APPLE__) && !defined(CURL_CA_BUNDLE) && !defined(CURL_CA_PATH)
  #  define CMAKE_FIND_CAFILE
  #  include "cmSystemTools.h"
 -#endif
+ #include "cmStringAlgorithms.h"
  
  // curl versions before 7.21.5 did not provide this error code
- #if defined(LIBCURL_VERSION_NUM) && LIBCURL_VERSION_NUM < 0x071505
-@@ -29,6 +26,19 @@ std::string cmCurlSetCAInfo(::CURL* curl
+@@ -30,6 +27,19 @@
      ::CURLcode res = ::curl_easy_setopt(curl, CURLOPT_CAINFO, cafile);
      check_curl_result(res, "Unable to set TLS/SSL Verify CAINFO: ");
    }