diff --git a/src/fitting/binding.jl b/src/fitting/binding.jl
index 3ff56adf..ecfa88a3 100644
--- a/src/fitting/binding.jl
+++ b/src/fitting/binding.jl
@@ -12,6 +12,8 @@ function _construct_bound_mapping(bindings, parameter_count)
         # the model we use as a reference to bind *to*
         reference = binding[1]
         for b in @views binding[2:end]
+            # get the number of the parameter that we are binding
+            parameter_number = parameter_mapping[b[1]][b[2]]
             parameter_mapping[b[1]][b[2]] = reference[2]
 
             # mark for removal: find the parameter index in the global array
@@ -21,11 +23,17 @@ function _construct_bound_mapping(bindings, parameter_count)
 
             # need to now shuffle all the indices greater than this one down by 1
             for k = b[2]+1:length(parameter_mapping[b[1]])
-                parameter_mapping[b[1]][k] -= 1
+                if (parameter_mapping[b[1]][k] > parameter_number)
+                    parameter_mapping[b[1]][k] -= 1
+                end
             end
             # and for subsequent models
             for j = b[1]+1:length(parameter_count)
-                parameter_mapping[j] .-= 1
+                for k = 1:length(parameter_mapping[j])
+                    if parameter_mapping[j][k] > parameter_number
+                        parameter_mapping[j][k] -= 1
+                    end
+                end
             end
         end
     end
diff --git a/test/fitting/test-binding.jl b/test/fitting/test-binding.jl
index 06f8ddfc..9e56ba00 100644
--- a/test/fitting/test-binding.jl
+++ b/test/fitting/test-binding.jl
@@ -54,3 +54,26 @@ values = trunc.(Int, get_value.(parameters))
 
 model1 = PowerLaw()
 model2 = PowerLaw() + PowerLaw()
+
+# test multiple bindings with multiple models and multiple datasets
+prob = FittingProblem(model1 => dummy_data1, model1 => dummy_data1, model1 => dummy_data1)
+bind!(prob, :K, :a)
+_, mapping = SpectralFitting._build_parameter_mapping(prob.model, prob.bindings)
+@test mapping == ([1, 2], [1, 2], [1, 2])
+
+# 3 models, 1 bound parameter
+prob = FittingProblem(model1 => dummy_data1, model1 => dummy_data1, model1 => dummy_data1)
+bind!(prob, :a)
+_, mapping = SpectralFitting._build_parameter_mapping(prob.model, prob.bindings)
+@test mapping == ([1, 2], [3, 2], [4, 2])
+
+# 3 models (2 the same, 1 different), bind one parameter between the two
+prob = FittingProblem(model1 => dummy_data1, model2 => dummy_data1, model1 => dummy_data1)
+bind!(prob, 1 => :a, 2 => :a_2, 3 => :a)
+_, mapping = SpectralFitting._build_parameter_mapping(prob.model, prob.bindings)
+@test mapping == ([1, 2], [3, 4, 5, 2], [6, 2])
+
+# 2 models, both different, bind a parameter that is only in one model (check it does no-ops okay)
+# prob = FittingProblem(model1 => dummy_data1, model2 => dummy_data1)
+# bind!(prob, :K)
+# note that this does not work at present because `_get_index_of_symbol` throws an error if the symbol is not found