diff --git a/recipes/sleef/all/CMakeLists.txt b/recipes/sleef/all/CMakeLists.txt
deleted file mode 100644
index bd3083b512cb9..0000000000000
--- a/recipes/sleef/all/CMakeLists.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-cmake_minimum_required(VERSION 3.1)
-project(cmake_wrapper)
-
-include(conanbuildinfo.cmake)
-conan_basic_setup()
-
-add_subdirectory(source_subfolder)
diff --git a/recipes/sleef/all/conandata.yml b/recipes/sleef/all/conandata.yml
index d1737a7a842cf..2cb4098c3fd69 100644
--- a/recipes/sleef/all/conandata.yml
+++ b/recipes/sleef/all/conandata.yml
@@ -1,4 +1,7 @@
 sources:
+  "3.6":
+    url: "https://github.com/shibatch/sleef/archive/3.6.tar.gz"
+    sha256: "de4f3d992cf2183a872cd397f517c1defcd3ee6cafa2ce5fa36963bd7e562446"
   "3.5.1":
     url: "https://github.com/shibatch/sleef/archive/3.5.1.tar.gz"
     sha256: "415ee9b1bcc5816989d3d4d92afd0cd3f9ee89cbd5a33eb008e69751e40438ab"
diff --git a/recipes/sleef/all/conanfile.py b/recipes/sleef/all/conanfile.py
index 0496b1b63c7cd..7cba3764e2337 100644
--- a/recipes/sleef/all/conanfile.py
+++ b/recipes/sleef/all/conanfile.py
@@ -1,19 +1,25 @@
-from conans import ConanFile, CMake, tools
-from conans.errors import ConanInvalidConfiguration
 import os
 
-required_conan_version = ">=1.32.0"
+from conan import ConanFile
+from conan.errors import ConanInvalidConfiguration
+from conan.tools.build import cross_building
+from conan.tools.cmake import CMake, CMakeToolchain, cmake_layout
+from conan.tools.env import VirtualBuildEnv
+from conan.tools.files import copy, get, rmdir
+from conan.tools.scm import Version
+
+required_conan_version = ">=1.53.0"
 
 
 class SleefConan(ConanFile):
     name = "sleef"
-    description = "SLEEF is a library that implements vectorized versions " \
-                  "of C standard math functions."
+    description = "SLEEF is a library that implements vectorized versions of C standard math functions."
     license = "BSL-1.0"
-    topics = ("conan", "sleef", "vectorization", "simd")
-    homepage = "https://sleef.org"
     url = "https://github.com/conan-io/conan-center-index"
+    homepage = "https://sleef.org"
+    topics = ("vectorization", "simd")
 
+    package_type = "library"
     settings = "os", "arch", "compiler", "build_type"
     options = {
         "shared": [True, False],
@@ -24,75 +30,92 @@ class SleefConan(ConanFile):
         "fPIC": True,
     }
 
-    short_paths = True
-
-    exports_sources = "CMakeLists.txt"
-    generators = "cmake"
-    _cmake = None
-
-    @property
-    def _source_subfolder(self):
-        return "source_subfolder"
-
-    @property
-    def _build_subfolder(self):
-        return "build_subfolder"
-
     def config_options(self):
         if self.settings.os == "Windows":
             del self.options.fPIC
 
     def configure(self):
         if self.options.shared:
-            del self.options.fPIC
-        del self.settings.compiler.libcxx
-        del self.settings.compiler.cppstd
+            self.options.rm_safe("fPIC")
+        self.settings.rm_safe("compiler.libcxx")
+        self.settings.rm_safe("compiler.cppstd")
+
+    def layout(self):
+        cmake_layout(self, src_folder="src")
 
     def validate(self):
         if self.settings.os == "Windows" and self.options.shared:
-            raise ConanInvalidConfiguration("shared sleef not supported on Windows, it produces runtime errors")
+            raise ConanInvalidConfiguration(
+                "shared sleef not supported on Windows, it produces runtime errors"
+            )
+        if self.settings.compiler == "apple-clang":
+            if cross_building(self):
+                # Fails with "No rule to make target `/bin/mkrename'"
+                # https://github.com/shibatch/sleef/issues/308
+                raise ConanInvalidConfiguration(f"{self.ref} does not support cross-building with apple-clang")
+            if Version(self.version) < "3.6" and self.settings.arch == "armv8":
+                # clang: error: the clang compiler does not support '-march=armv7-a'
+                # clang: warning: argument unused during compilation: '-mfpu=vfpv4' [-Wunused-command-line-argument]
+                # clang: warning: argument unused during compilation: '-arch arm64' [-Wunused-command-line-argument]
+                # clang: warning: argument unused during compilation: '-mmacosx-version-min=11.0' [-Wunused-command-line-argument]
+                raise ConanInvalidConfiguration(f"{self.ref} does not support Mac M1. Please, use {self.name} version >=3.6.")
+
+    def build_requirements(self):
+        if Version(self.version) >= "3.6":
+            self.tool_requires("cmake/[>=3.18 <4]")
 
     def source(self):
-        tools.get(**self.conan_data["sources"][self.version])
-        os.rename(self.name + "-" + self.version, self._source_subfolder)
-
-    def _configure_cmake(self):
-        if self._cmake:
-            return self._cmake
-        self._cmake = CMake(self)
-        self._cmake.definitions["BUILD_STATIC_TEST_BINS"] = False
-        self._cmake.definitions["ENABLE_LTO"] = False
-        self._cmake.definitions["BUILD_LIBM"] = True
-        self._cmake.definitions["BUILD_DFT"] = False
-        self._cmake.definitions["BUILD_QUAD"] = False
-        self._cmake.definitions["BUILD_GNUABI_LIBS"] = False
-        self._cmake.definitions["BUILD_TESTS"] = False
-        self._cmake.definitions["BUILD_INLINE_HEADERS"] = False
-        self._cmake.definitions["SLEEF_TEST_ALL_IUT"] = False
-        self._cmake.definitions["SLEEF_SHOW_CONFIG"] = True
-        self._cmake.definitions["SLEEF_SHOW_ERROR_LOG"] = False
-        self._cmake.definitions["ENFORCE_TESTER"] = False
-        self._cmake.definitions["ENFORCE_TESTER3"] = False
-        self._cmake.definitions["ENABLE_ALTDIV"] = False
-        self._cmake.definitions["ENABLE_ALTSQRT"] = False
-        self._cmake.definitions["DISABLE_FFTW"] = True
-        self._cmake.configure(build_folder=self._build_subfolder)
-        return self._cmake
+        get(self, **self.conan_data["sources"][self.version], strip_root=True)
+
+    def generate(self):
+        VirtualBuildEnv(self).generate()
+
+        tc = CMakeToolchain(self)
+        tc.cache_variables["BUILD_SHARED_LIBS"] = self.options.shared
+        if Version(self.version) >= "3.6":
+            tc.cache_variables["SLEEF_BUILD_STATIC_TEST_BINS"] = False
+            tc.cache_variables["SLEEF_BUILD_LIBM"] = True
+            tc.cache_variables["SLEEF_BUILD_DFT"] = False
+            tc.cache_variables["SLEEF_BUILD_QUAD"] = False
+            tc.cache_variables["SLEEF_BUILD_GNUABI_LIBS"] = False
+            tc.cache_variables["SLEEF_BUILD_SCALAR_LIB"] = False
+            tc.cache_variables["SLEEF_BUILD_TESTS"] = False
+            tc.cache_variables["SLEEF_BUILD_INLINE_HEADERS"] = False
+            tc.cache_variables["SLEEF_SHOW_CONFIG"] = True
+            tc.cache_variables["SLEEF_SHOW_ERROR_LOG"] = False
+            tc.cache_variables["SLEEF_ENABLE_ALTDIV"] = False
+            tc.cache_variables["SLEEF_ENABLE_ALTSQRT"] = False
+            tc.cache_variables["SLEEF_DISABLE_FFTW"] = True
+            tc.cache_variables["SLEEF_DISABLE_MPFR"] = True
+            tc.cache_variables["SLEEF_DISABLE_SSL"] = True
+            tc.cache_variables["SLEEF_ENABLE_CUDA"] = False
+            tc.cache_variables["SLEEF_ENABLE_CXX"] = False
+        else:
+            tc.cache_variables["BUILD_DFT"] = False
+            tc.cache_variables["BUILD_GNUABI_LIBS"] = False
+            tc.cache_variables["BUILD_TESTS"] = False
+            tc.cache_variables["DISABLE_FFTW"] = True
+        tc.generate()
 
     def build(self):
-        cmake = self._configure_cmake()
+        cmake = CMake(self)
+        cmake.configure()
         cmake.build()
 
     def package(self):
-        self.copy("LICENSE.txt", dst="licenses", src=self._source_subfolder)
-        cmake = self._configure_cmake()
+        copy(self, "LICENSE.txt",
+             dst=os.path.join(self.package_folder, "licenses"),
+             src=self.source_folder)
+        cmake = CMake(self)
         cmake.install()
-        tools.rmdir(os.path.join(self.package_folder, "lib", "pkgconfig"))
+        rmdir(self, os.path.join(self.package_folder, "lib", "pkgconfig"))
+        rmdir(self, os.path.join(self.package_folder, "lib", "cmake"))
+        rmdir(self, os.path.join(self.package_folder, "dummy"))
 
     def package_info(self):
-        self.cpp_info.names["pkg_config"] = "sleef"
+        self.cpp_info.set_property("pkg_config_name", "sleef")
         self.cpp_info.libs = ["sleef"]
         if self.settings.os == "Windows" and not self.options.shared:
             self.cpp_info.defines = ["SLEEF_STATIC_LIBS"]
-        if self.settings.os == "Linux":
+        if self.settings.os in ["Linux", "FreeBSD"]:
             self.cpp_info.system_libs = ["m"]
diff --git a/recipes/sleef/all/test_package/CMakeLists.txt b/recipes/sleef/all/test_package/CMakeLists.txt
index 7b9b613cbb24a..a5f1ed24ef5f7 100644
--- a/recipes/sleef/all/test_package/CMakeLists.txt
+++ b/recipes/sleef/all/test_package/CMakeLists.txt
@@ -1,8 +1,7 @@
-cmake_minimum_required(VERSION 3.1)
+cmake_minimum_required(VERSION 3.15)
 project(test_package C)
 
-include(${CMAKE_BINARY_DIR}/conanbuildinfo.cmake)
-conan_basic_setup()
+find_package(sleef REQUIRED CONFIG)
 
 add_executable(${PROJECT_NAME} test_package.c)
-target_link_libraries(${PROJECT_NAME} ${CONAN_LIBS})
+target_link_libraries(${PROJECT_NAME} PRIVATE sleef::sleef)
diff --git a/recipes/sleef/all/test_package/conanfile.py b/recipes/sleef/all/test_package/conanfile.py
index 5216332f39f5c..ef5d7042163ec 100644
--- a/recipes/sleef/all/test_package/conanfile.py
+++ b/recipes/sleef/all/test_package/conanfile.py
@@ -1,10 +1,19 @@
-from conans import ConanFile, CMake, tools
+from conan import ConanFile
+from conan.tools.build import can_run
+from conan.tools.cmake import cmake_layout, CMake
 import os
 
 
 class TestPackageConan(ConanFile):
     settings = "os", "arch", "compiler", "build_type"
-    generators = "cmake"
+    generators = "CMakeDeps", "CMakeToolchain", "VirtualRunEnv"
+    test_type = "explicit"
+
+    def requirements(self):
+        self.requires(self.tested_reference_str)
+
+    def layout(self):
+        cmake_layout(self)
 
     def build(self):
         cmake = CMake(self)
@@ -12,6 +21,6 @@ def build(self):
         cmake.build()
 
     def test(self):
-        if not tools.cross_building(self.settings):
-            bin_path = os.path.join("bin", "test_package")
-            self.run(bin_path, run_environment=True)
+        if can_run(self):
+            bin_path = os.path.join(self.cpp.build.bindir, "test_package")
+            self.run(bin_path, env="conanrun")
diff --git a/recipes/sleef/all/test_v1_package/CMakeLists.txt b/recipes/sleef/all/test_v1_package/CMakeLists.txt
new file mode 100644
index 0000000000000..91630d79f4abb
--- /dev/null
+++ b/recipes/sleef/all/test_v1_package/CMakeLists.txt
@@ -0,0 +1,8 @@
+cmake_minimum_required(VERSION 3.15)
+project(test_package)
+
+include(${CMAKE_BINARY_DIR}/conanbuildinfo.cmake)
+conan_basic_setup(TARGETS)
+
+add_subdirectory(${CMAKE_CURRENT_SOURCE_DIR}/../test_package/
+                 ${CMAKE_CURRENT_BINARY_DIR}/test_package/)
diff --git a/recipes/sleef/all/test_v1_package/conanfile.py b/recipes/sleef/all/test_v1_package/conanfile.py
new file mode 100644
index 0000000000000..a9f777f7680ff
--- /dev/null
+++ b/recipes/sleef/all/test_v1_package/conanfile.py
@@ -0,0 +1,17 @@
+from conans import ConanFile, CMake, tools
+import os
+
+
+class TestPackageConan(ConanFile):
+    settings = "os", "arch", "compiler", "build_type"
+    generators = "cmake", "cmake_find_package_multi"
+
+    def build(self):
+        cmake = CMake(self)
+        cmake.configure()
+        cmake.build()
+
+    def test(self):
+        if not tools.cross_building(self.settings):
+            bin_path = os.path.join("bin", "test_package")
+            self.run(bin_path, run_environment=True)
diff --git a/recipes/sleef/config.yml b/recipes/sleef/config.yml
index 2276d8a2cd6a8..3c718426b97bd 100644
--- a/recipes/sleef/config.yml
+++ b/recipes/sleef/config.yml
@@ -1,3 +1,5 @@
 versions:
+  "3.6":
+    folder: all
   "3.5.1":
     folder: all