diff --git a/Source/cmFindPackageCommand.cxx b/Source/cmFindPackageCommand.cxx
index f17002e63..3541ca39e 100644
--- a/Source/cmFindPackageCommand.cxx
+++ b/Source/cmFindPackageCommand.cxx
@@ -952,11 +952,26 @@ bool cmFindPackageCommand::HandlePackageMode()
       }
     }
 
+  std::string foundVar = this->Name;
+  foundVar += "_FOUND";
+
   // If the directory for the config file was found, try to read the file.
   bool result = true;
   bool found = false;
+  bool configFileSetFOUNDFalse = false;
+
   if(fileFound)
     {
+    if ((this->Makefile->IsDefinitionSet(foundVar.c_str()))
+      && (this->Makefile->IsOn(foundVar.c_str()) == false))
+      {
+      // by removing Foo_FOUND here if it is FALSE, we don't really change
+      // the situation for the Config file which is about to be included,
+      // but we make it possible to detect later on whether the Config file
+      // has set Foo_FOUND to FALSE itself:
+      this->Makefile->RemoveDefinition(foundVar.c_str());
+      }
+
     // Set the version variables before loading the config file.
     // It may override them.
     this->StoreVersionFound();
@@ -966,6 +981,15 @@ bool cmFindPackageCommand::HandlePackageMode()
       {
       // The package has been found.
       found = true;
+
+      // Check whether the Config file has set Foo_FOUND to FALSE:
+      if ((this->Makefile->IsDefinitionSet(foundVar.c_str()))
+           && (this->Makefile->IsOn(foundVar.c_str()) == false))
+        {
+        // we get here if the Config file has set Foo_FOUND actively to FALSE
+        found = false;
+        configFileSetFOUNDFalse = true;
+        }
       }
     else
       {
@@ -973,14 +997,22 @@ bool cmFindPackageCommand::HandlePackageMode()
       result = false;
       }
     }
-  else if(!this->Quiet || this->Required)
+
+  if (result && !found && (!this->Quiet || this->Required))
     {
     // The variable is not set.
     cmOStringStream e;
     cmOStringStream aw;
+    if (configFileSetFOUNDFalse)
+      {
+      e << "Found package configuration file:\n"
+        "  " << this->FileFound << "\n"
+        "but it set " << foundVar << " to FALSE so package \"" <<
+        this->Name << "\" is considered to be NOT FOUND.";
+      }
     // If there are files in ConsideredConfigs, it means that FooConfig.cmake
     // have been found, but they didn't have appropriate versions.
-    if (this->ConsideredConfigs.size() > 0)
+    else if (this->ConsideredConfigs.size() > 0)
       {
       e << "Could not find a configuration file for package \""
         << this->Name << "\" that "
@@ -1074,8 +1106,6 @@ bool cmFindPackageCommand::HandlePackageMode()
     }
 
   // Set a variable marking whether the package was found.
-  std::string foundVar = this->Name;
-  foundVar += "_FOUND";
   this->Makefile->AddDefinition(foundVar.c_str(), found? "1":"0");
 
   // Set a variable naming the configuration file that was found.
diff --git a/Tests/FindPackageTest/CMakeLists.txt b/Tests/FindPackageTest/CMakeLists.txt
index 73f24e0bd..eba9db9e1 100644
--- a/Tests/FindPackageTest/CMakeLists.txt
+++ b/Tests/FindPackageTest/CMakeLists.txt
@@ -82,6 +82,7 @@ SET(PACKAGES
   RecursiveA RecursiveB RecursiveC
   ArchA ArchB ArchC ArchD
   EnvA EnvB
+  SetFoundTRUE SetFoundFALSE
   ${CMakeTestSystemPackage}
   )
 FOREACH(p ${PACKAGES})
@@ -117,6 +118,10 @@ FIND_PACKAGE(VersionedC 4.0 EXACT NAMES zot)
 FIND_PACKAGE(VersionedD 1.1 EXACT NAMES Baz)
 FIND_PACKAGE(VersionedE 1.2 EXACT NAMES Baz)
 
+# Test Config files which set Xyz_FOUND themselves:
+FIND_PACKAGE(SetFoundTRUE NO_MODULE)
+FIND_PACKAGE(SetFoundFALSE NO_MODULE)
+
 # Test wrong initial path when result is present.
 SET(WrongA_DIR "${VersionedD_DIR}")
 FIND_PACKAGE(WrongA 1.2 EXACT NAMES Baz)
@@ -201,6 +206,8 @@ SET(ArchC_EXPECTED "lib/arch/zot-3.1/zot-config.cmake")
 SET(ArchD_EXPECTED "lib/arch/cmake/zot-4.0/zot-config.cmake")
 SET(EnvA_EXPECTED "lib/zot-3.1/zot-config.cmake")
 SET(EnvB_MISSING "EnvB_DIR-NOTFOUND")
+SET(SetFoundTRUE_EXPECTED "cmake/SetFoundTRUEConfig.cmake")
+SET(SetFoundFALSE_MISSING "${CMAKE_CURRENT_SOURCE_DIR}/cmake")
 SET(CMakeTestSystemPackage_EXPECTED "SystemPackage/CMakeTestSystemPackageConfig.cmake")
 
 # Check the results.
@@ -212,6 +219,11 @@ FOREACH(p ${PACKAGES})
         "Package ${p} should have been [${${p}_MISSING}] but "
         "was [${${p}_DIR}]")
     ENDIF()
+    IF(${p}_FOUND)
+      MESSAGE(SEND_ERROR
+        "Package ${p} should not have been found, but ${p}_FOUND is set to "
+        "\"${${p}_FOUND}\"")
+    ENDIF()
   ELSEIF(${p}_FOUND)
     # Convert to relative path for comparison to expected location.
     FILE(RELATIVE_PATH REL_${p}_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}"
diff --git a/Tests/FindPackageTest/cmake/SetFoundFALSEConfig.cmake b/Tests/FindPackageTest/cmake/SetFoundFALSEConfig.cmake
new file mode 100644
index 000000000..ae6bd1454
--- /dev/null
+++ b/Tests/FindPackageTest/cmake/SetFoundFALSEConfig.cmake
@@ -0,0 +1 @@
+set(SetFoundFALSE_FOUND FALSE)
diff --git a/Tests/FindPackageTest/cmake/SetFoundTRUEConfig.cmake b/Tests/FindPackageTest/cmake/SetFoundTRUEConfig.cmake
new file mode 100644
index 000000000..19d071144
--- /dev/null
+++ b/Tests/FindPackageTest/cmake/SetFoundTRUEConfig.cmake
@@ -0,0 +1 @@
+set(SetFoundTRUE_FOUND TRUE)
diff --git a/Tests/RunCMake/find_package/RunCMakeTest.cmake b/Tests/RunCMake/find_package/RunCMakeTest.cmake
index ba57f99e8..34fa73322 100644
--- a/Tests/RunCMake/find_package/RunCMakeTest.cmake
+++ b/Tests/RunCMake/find_package/RunCMakeTest.cmake
@@ -12,3 +12,4 @@ run_cmake(MissingConfigOneName)
 run_cmake(MissingConfigRequired)
 run_cmake(MissingConfigVersion)
 run_cmake(MixedModeOptions)
+run_cmake(SetFoundFALSE)
diff --git a/Tests/RunCMake/find_package/SetFoundFALSE-stderr.txt b/Tests/RunCMake/find_package/SetFoundFALSE-stderr.txt
new file mode 100644
index 000000000..695f6450d
--- /dev/null
+++ b/Tests/RunCMake/find_package/SetFoundFALSE-stderr.txt
@@ -0,0 +1,9 @@
+CMake Warning at SetFoundFALSE.cmake:2 \(find_package\):
+  Found package configuration file:
+
+    .*/Tests/RunCMake/find_package/SetFoundFALSEConfig.cmake
+
+  but it set SetFoundFALSE_FOUND to FALSE so package "SetFoundFALSE" is
+  considered to be NOT FOUND.
+Call Stack \(most recent call first\):
+  CMakeLists.txt:3 \(include\)
diff --git a/Tests/RunCMake/find_package/SetFoundFALSE.cmake b/Tests/RunCMake/find_package/SetFoundFALSE.cmake
new file mode 100644
index 000000000..fbcec3c56
--- /dev/null
+++ b/Tests/RunCMake/find_package/SetFoundFALSE.cmake
@@ -0,0 +1,2 @@
+set(SetFoundFALSE_DIR "${CMAKE_CURRENT_SOURCE_DIR}")
+find_package(SetFoundFALSE CONFIG)
diff --git a/Tests/RunCMake/find_package/SetFoundFALSEConfig.cmake b/Tests/RunCMake/find_package/SetFoundFALSEConfig.cmake
new file mode 100644
index 000000000..ae6bd1454
--- /dev/null
+++ b/Tests/RunCMake/find_package/SetFoundFALSEConfig.cmake
@@ -0,0 +1 @@
+set(SetFoundFALSE_FOUND FALSE)