diff --git a/pmd-java/src/main/java/net/sourceforge/pmd/lang/java/rule/bestpractices/UnusedImportsRule.java b/pmd-java/src/main/java/net/sourceforge/pmd/lang/java/rule/bestpractices/UnusedImportsRule.java
index f7307a2a39..c4507a820d 100644
--- a/pmd-java/src/main/java/net/sourceforge/pmd/lang/java/rule/bestpractices/UnusedImportsRule.java
+++ b/pmd-java/src/main/java/net/sourceforge/pmd/lang/java/rule/bestpractices/UnusedImportsRule.java
@@ -143,6 +143,23 @@ public class UnusedImportsRule extends AbstractJavaRule {
 
     @Override
     public Object visit(ASTName node, Object data) {
+        if (isMethodCall(node) && isQualifiedName(node)) {
+            String name = node.getImage().substring(0, node.getImage().lastIndexOf('.'));
+            // try to resolve with on demand imports...
+            ClassTypeResolver classTypeResolver = node.getFirstParentOfType(ASTCompilationUnit.class).getClassTypeResolver();
+            Iterator<ImportWrapper> it = imports.iterator();
+            while (it.hasNext()) {
+                ImportWrapper i = it.next();
+                if (i.getName() == null) {
+                    String fullName = i.getFullName() + "." + name;
+                    if (classTypeResolver.loadClass(fullName) != null) {
+                        // found a match
+                        it.remove();
+                        return data;
+                    }
+                }
+            }
+        }
         check(node);
         return data;
     }
diff --git a/pmd-java/src/test/java/net/sourceforge/pmd/lang/java/rule/bestpractices/unusedimports/Issue2016.java b/pmd-java/src/test/java/net/sourceforge/pmd/lang/java/rule/bestpractices/unusedimports/Issue2016.java
new file mode 100644
index 0000000000..db0dc08a99
--- /dev/null
+++ b/pmd-java/src/test/java/net/sourceforge/pmd/lang/java/rule/bestpractices/unusedimports/Issue2016.java
@@ -0,0 +1,17 @@
+/**
+ * BSD-style license; for more info see http://pmd.sourceforge.net/license.html
+ */
+
+package net.sourceforge.pmd.lang.java.rule.bestpractices.unusedimports;
+
+import java.util.*;
+
+/**
+ * Note: In order for this test case to work, the class "Issue2016" must also be compiled and available
+ * on the auxclasspath.
+ */
+public class Issue2016 {
+    public void testFunction() {
+        Objects.toString(null);
+    }
+}
diff --git a/pmd-java/src/test/resources/net/sourceforge/pmd/lang/java/rule/bestpractices/xml/UnusedImports.xml b/pmd-java/src/test/resources/net/sourceforge/pmd/lang/java/rule/bestpractices/xml/UnusedImports.xml
index 3c1ce4c2f9..4a0b42a568 100644
--- a/pmd-java/src/test/resources/net/sourceforge/pmd/lang/java/rule/bestpractices/xml/UnusedImports.xml
+++ b/pmd-java/src/test/resources/net/sourceforge/pmd/lang/java/rule/bestpractices/xml/UnusedImports.xml
@@ -531,4 +531,24 @@ public class VendingV2PaymentRequest {
 }	
         ]]></code>
     </test-code>
+
+    <test-code>
+        <description>#2016 [java] UnusedImports: False positive if wildcard is used and only static methods</description>
+        <expected-problems>0</expected-problems>
+        <code><![CDATA[
+package net.sourceforge.pmd.lang.java.rule.bestpractices.unusedimports;
+
+import java.util.*;
+
+/**
+ * Note: In order for this test case to work, the class "Issue2016" must also be compiled and available
+ * on the auxclasspath.
+ */
+public class Issue2016 {
+    public void testFunction() {
+        Objects.toString(null);
+    }
+}
+        ]]></code>
+    </test-code>
 </test-data>