diff --git a/lib/rdf/spec/queryable.rb b/lib/rdf/spec/queryable.rb
index 0b23bf8..76954fc 100644
--- a/lib/rdf/spec/queryable.rb
+++ b/lib/rdf/spec/queryable.rb
@@ -85,26 +85,31 @@
           expect(solutions.size).to eq @statements.size
         end
 
-        it "returns statements from unnamed graphss with false graph_name" do
+        it "returns statements from unnamed graphs with false graph_name" do
           pattern = RDF::Query::Pattern.new(nil, nil, nil, graph_name: false)
           solutions = []
           subject.send(method, pattern) {|s| solutions << s}
-          named_statements = subject.statements.reject {|st| st.has_name?}.length
-          expect(solutions.size).to eq named_statements
+
+          named_statements = subject.statements
+          named_statements.reject! {|st| st.has_name?} unless
+            subject.respond_to?(:graph_name) && !subject.graph_name.nil?
+
+          expect(solutions.size).to eq named_statements.size
         end
 
-        it "returns statements from named graphss with variable graph_name" do
+        it "returns statements from named graphs with variable graph_name" do
           unless subject.graph_names.to_a.empty?
             pattern = RDF::Query::Pattern.new(nil, nil, nil, graph_name: :c)
             solutions = []
             subject.send(method, pattern) {|s| solutions << s}
-            named_statements = subject.statements.select {|st| st.has_name?}.length
-            expect(solutions.size).to eq named_statements
+            named_statements = subject.statements.select {|st| st.has_name?}
+            expect(solutions.size).to eq named_statements.size
           end
         end
 
         it "returns statements from specific graph with URI graph_name" do
-          unless subject.graph_names.to_a.empty?
+          unless subject.graph_names.to_a.empty? || 
+                 (subject.respond_to?(:graph_name) && !subject.graph_name.nil?)
             pattern = RDF::Query::Pattern.new(nil, nil, nil, graph_name: RDF::URI("http://ar.to/#self"))
             solutions = []
             subject.send(method, pattern) {|s| solutions << s}
diff --git a/lib/rdf/spec/transaction.rb b/lib/rdf/spec/transaction.rb
index 5685c3a..65a7d8c 100644
--- a/lib/rdf/spec/transaction.rb
+++ b/lib/rdf/spec/transaction.rb
@@ -20,9 +20,29 @@
     require 'rdf/spec/queryable'
     let(:queryable) do
       repository.insert(*RDF::Spec.quads)
-      q = klass.new(repository, mutable: true)
+      klass.new(repository)
     end
     it_behaves_like 'an RDF::Queryable'
+
+    context 'with a graph_name' do
+      let(:queryable) do
+        graph_name = RDF::URI('g')
+        graph = RDF::Graph.new(graph_name: graph_name, data: repository)
+        graph.insert(*RDF::Spec.quads)
+        klass.new(repository, graph_name: graph_name)
+      end
+      it_behaves_like 'an RDF::Queryable'
+    end
+
+    context 'with a false graph_name' do
+      let(:queryable) do
+        graph = RDF::Graph.new(data: repository)
+        graph.insert(*RDF::Spec.quads)
+        graph_name = false
+        klass.new(repository, graph_name: graph_name)
+      end
+      it_behaves_like 'an RDF::Queryable'
+    end
   end
 
   describe "#initialize" do
@@ -128,17 +148,17 @@
         expect(subject.repository).to have_statement(st)
       end
 
-      it 'retains existing graph names' do
+      it 'overwrites existing graph names' do
         st.graph_name = RDF::URI('g')
         repository.insert(st)
         
         expect do 
           subject.delete(st)
           subject.execute
-        end.to change { subject.repository.statements }.to be_empty
+        end.not_to change { subject.repository.statements }
       end
 
-      it 'retains existing default graph name' do
+      it 'overwrites existing default graph name' do
         st.graph_name = false
 
         repository.insert(st)
@@ -146,7 +166,7 @@
         expect do 
           subject.delete(st)
           subject.execute
-        end.to change { subject.repository.statements }.to be_empty
+        end.not_to change { subject.repository.statements }
       end
     end
   end
@@ -200,26 +220,32 @@
         expect(subject.repository).to have_statement(with_name)
       end
 
-      it 'retains existing graph names' do
+      it 'overwrites existing graph names' do
         st.graph_name = RDF::URI('g')
-        
+        with_name = st.dup
+        with_name.graph_name = graph_uri
+
         expect do 
           subject.insert(st)
           subject.execute
         end.to change { subject.repository.statements }
 
-        expect(subject.repository).to have_statement(st)
+        expect(subject.repository).not_to have_statement(st)
+        expect(subject.repository).to have_statement(with_name)
       end
 
-      it 'retains existing default graph name' do
+      it 'overwrites existing default graph name' do
         st.graph_name = false
-        
-        expect do 
+        with_name = st.dup
+        with_name.graph_name = graph_uri
+
+        expect do
           subject.insert(st)
           subject.execute
         end.to change { subject.repository.statements }
-
-        expect(subject.repository).to have_statement(st)
+        
+        expect(subject.repository).not_to have_statement(st)
+        expect(subject.repository).to have_statement(with_name)
       end
     end
   end