diff --git a/mining/src/main/java/amie/mining/assistant/DefaultMiningAssistant.java b/mining/src/main/java/amie/mining/assistant/DefaultMiningAssistant.java
index 6f36b3f..90841e9 100644
--- a/mining/src/main/java/amie/mining/assistant/DefaultMiningAssistant.java
+++ b/mining/src/main/java/amie/mining/assistant/DefaultMiningAssistant.java
@@ -248,9 +248,13 @@ public void getDanglingAtoms(Rule query, double minCardinality, Collection<Rule>
 		// Pruning by maximum length for the \mathcal{O}_D operator.
 		if(query.getRealLength() == this.maxDepth - 1) {
 			if (this.exploitMaxLengthOption) {
-				if(!query.getOpenVariables().isEmpty() 
-						&& !this.allowConstants 
-						&& !this.enforceConstants) {
+				if (query.getOpenVariables().size() > 1) {
+					// There will be more than 2 open variables and we will not be able to close all of them.
+					return;
+				}
+
+				if (!canAddInstantiatedAtoms()) {
+					// We can't count on instantiation operator to close the new dangling variable.
 					return;
 				}
 			}
diff --git a/mining/src/main/java/amie/mining/assistant/MiningAssistant.java b/mining/src/main/java/amie/mining/assistant/MiningAssistant.java
index a5087b7..60a6ab5 100644
--- a/mining/src/main/java/amie/mining/assistant/MiningAssistant.java
+++ b/mining/src/main/java/amie/mining/assistant/MiningAssistant.java
@@ -600,7 +600,13 @@ public void getDanglingAtoms(Rule rule, double minSupportThreshold, Collection<R
 
 		if (exploitMaxLengthOption) {
 			if(rule.getRealLength() == maxDepth - 1){
-				if(!rule.getOpenVariables().isEmpty() && !allowConstants){
+				if (rule.getOpenVariables().size() > 1) {
+					// There will be more than 2 open variables and we will not be able to close all of them.
+					return;
+				}
+
+				if (!canAddInstantiatedAtoms()) {
+					// We can't count on instantiation operator to close the new dangling variable.
 					return;
 				}
 			}
diff --git a/mining/src/main/java/amie/mining/assistant/experimental/SeedsCountMiningAssistant.java b/mining/src/main/java/amie/mining/assistant/experimental/SeedsCountMiningAssistant.java
index c8d0ef4..0ef5176 100644
--- a/mining/src/main/java/amie/mining/assistant/experimental/SeedsCountMiningAssistant.java
+++ b/mining/src/main/java/amie/mining/assistant/experimental/SeedsCountMiningAssistant.java
@@ -206,9 +206,13 @@ public void getDanglingAtoms(Rule query, double minCardinality, Collection<Rule>
 		//General case
 		if(query.getLength() == maxDepth - 1) {
 			if (this.exploitMaxLengthOption) {
-				if(!openVariables.isEmpty() 
-						&& !this.allowConstants 
-						&& !this.enforceConstants) {
+				if (query.getOpenVariables().size() > 1) {
+					// There will be more than 2 open variables and we will not be able to close all of them.
+					return;
+				}
+
+				if (!canAddInstantiatedAtoms()) {
+					// We can't count on instantiation operator to close the new dangling variable.
 					return;
 				}
 			}