diff --git a/.gitignore b/.gitignore
index 24c76a900..3900f0e3a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -7,6 +7,9 @@ tests/resources/PE2017
 # Dask
 dask-worker-space/
 
+# virtualenv
+bin/
+pyvenv.cfg
 
 # TIMP data
 *.RData
diff --git a/glotaran/builtin/io/yml/test/test_model_parser_kinetic.py b/glotaran/builtin/io/yml/test/test_model_parser_kinetic.py
index b9cfee392..ac621fd38 100644
--- a/glotaran/builtin/io/yml/test/test_model_parser_kinetic.py
+++ b/glotaran/builtin/io/yml/test/test_model_parser_kinetic.py
@@ -123,7 +123,7 @@ def test_irf(model):
             assert irf.width_dispersion == want
             want = [9]
             assert irf.scale == want
-        assert not irf.normalize
+        assert irf.normalize == (i == 1)
 
         if i == 2:
             assert irf.backsweep
diff --git a/glotaran/builtin/io/yml/test/test_model_spec_kinetic.yml b/glotaran/builtin/io/yml/test/test_model_spec_kinetic.yml
index 30cf67106..33b8c7058 100644
--- a/glotaran/builtin/io/yml/test/test_model_spec_kinetic.yml
+++ b/glotaran/builtin/io/yml/test/test_model_spec_kinetic.yml
@@ -56,7 +56,7 @@ megacomplex:
       k_matrix: [km1] # A megacomplex has one or more k-matrices
   cmplx2:
       k_matrix: [km2]
-  cmplx3: [[km3], None]
+  cmplx3: [[km3]]
 
 spectral_constraints:
   - type: zero
diff --git a/glotaran/builtin/models/kinetic_image/initial_concentration.py b/glotaran/builtin/models/kinetic_image/initial_concentration.py
index 35cce612e..1d6d952f4 100644
--- a/glotaran/builtin/models/kinetic_image/initial_concentration.py
+++ b/glotaran/builtin/models/kinetic_image/initial_concentration.py
@@ -6,7 +6,6 @@
 
 import numpy as np
 
-from glotaran.model import DatasetDescriptor
 from glotaran.model import model_attribute
 from glotaran.parameter import Parameter
 
@@ -22,16 +21,8 @@ class InitialConcentration:
     """An initial concentration describes the population of the compartments at
     the beginning of an experiment."""
 
-    def normalized(self, dataset: DatasetDescriptor) -> InitialConcentration:
-        parameters = self.parameters
-        for megacomplex in dataset.megacomplex:
-            scale = [
-                megacomplex.scale
-                if c in megacomplex.involved_compartments and megacomplex.scale
-                else 1
-                for c in self.compartments
-            ]
-            parameters = np.multiply(parameters, scale)
+    def normalized(self) -> InitialConcentration:
+        parameters = np.array(self.parameters)
         idx = [c not in self.exclude_from_normalize for c in self.compartments]
         parameters[idx] /= np.sum(parameters[idx])
         new = copy.deepcopy(self)
diff --git a/glotaran/builtin/models/kinetic_image/irf.py b/glotaran/builtin/models/kinetic_image/irf.py
index c6d6f473f..85a80e876 100644
--- a/glotaran/builtin/models/kinetic_image/irf.py
+++ b/glotaran/builtin/models/kinetic_image/irf.py
@@ -19,7 +19,7 @@ class IrfMeasured:
         "center": List[Parameter],
         "width": List[Parameter],
         "scale": {"type": List[Parameter], "allow_none": True},
-        "normalize": {"type": bool, "default": False},
+        "normalize": {"type": bool, "default": True},
         "backsweep": {"type": bool, "default": False},
         "backsweep_period": {"type": Parameter, "allow_none": True},
     },
diff --git a/glotaran/builtin/models/kinetic_image/k_matrix.py b/glotaran/builtin/models/kinetic_image/k_matrix.py
index 3a47be566..fe939085b 100644
--- a/glotaran/builtin/models/kinetic_image/k_matrix.py
+++ b/glotaran/builtin/models/kinetic_image/k_matrix.py
@@ -49,12 +49,14 @@ def involved_compartments(self) -> list[str]:
     def combine(self, k_matrix: KMatrix) -> KMatrix:
         """Creates a combined matrix.
 
+        When combining k-matrices km1 and km2 (km1.combine(km2)),
+        entries in km1 will be overwritten by corresponding entries in km2.
+
         Parameters
         ----------
         k_matrix :
             KMatrix to combine with.
 
-
         Returns
         -------
         combined :
@@ -63,9 +65,9 @@ def combine(self, k_matrix: KMatrix) -> KMatrix:
         """
         if not isinstance(k_matrix, KMatrix):
             raise TypeError("K-Matrices can only be combined with other K-Matrices.")
-        combined_matrix = {entry: k_matrix.matrix[entry] for entry in k_matrix.matrix}
-        for entry in self.matrix:
-            combined_matrix[entry] = self.matrix[entry]
+        combined_matrix = {entry: self.matrix[entry] for entry in self.matrix}
+        for entry in k_matrix.matrix:
+            combined_matrix[entry] = k_matrix.matrix[entry]
         combined = KMatrix()
         combined.label = f"{self.label}+{k_matrix.label}"
         combined.matrix = combined_matrix
diff --git a/glotaran/builtin/models/kinetic_image/kinetic_image_dataset_descriptor.py b/glotaran/builtin/models/kinetic_image/kinetic_image_dataset_descriptor.py
index 1bf07a405..36e92e258 100644
--- a/glotaran/builtin/models/kinetic_image/kinetic_image_dataset_descriptor.py
+++ b/glotaran/builtin/models/kinetic_image/kinetic_image_dataset_descriptor.py
@@ -12,11 +12,32 @@
     }
 )
 class KineticImageDatasetDescriptor(DatasetDescriptor):
-    def get_k_matrices(self):
-        return [mat for mat in [cmplx.full_k_matrix() for cmplx in self.megacomplex] if mat]
+    def get_megacomplex_k_matrices(self):
+        scales = (
+            [
+                self.megacomplex_scale[i]
+                for i, megacomplex in enumerate(self.megacomplex)
+                if megacomplex.has_k_matrix()
+            ]
+            if self.megacomplex_scale is not None
+            else None
+        )
+
+        matrices = [
+            megacomplex.full_k_matrix()
+            for megacomplex in self.megacomplex
+            if megacomplex.has_k_matrix()
+        ]
+
+        return scales, matrices
+
+    def has_k_matrix(self) -> bool:
+        _, k_matrices = self.get_megacomplex_k_matrices()
+        return len(k_matrices) != 0
 
     def compartments(self):
         compartments = []
-        for k in self.get_k_matrices():
+        _, k_matrices = self.get_megacomplex_k_matrices()
+        for k in k_matrices:
             compartments += k.involved_compartments()
         return list(set(compartments))
diff --git a/glotaran/builtin/models/kinetic_image/kinetic_image_matrix.py b/glotaran/builtin/models/kinetic_image/kinetic_image_matrix.py
index e02690e77..594a69698 100644
--- a/glotaran/builtin/models/kinetic_image/kinetic_image_matrix.py
+++ b/glotaran/builtin/models/kinetic_image/kinetic_image_matrix.py
@@ -20,7 +20,7 @@ def kinetic_matrix(
 
     compartments = None
     matrix = None
-    k_matrices = dataset_descriptor.get_k_matrices()
+    megacomplex_scales, k_matrices = dataset_descriptor.get_megacomplex_k_matrices()
 
     if len(k_matrices) == 0:
         return (None, None)
@@ -29,9 +29,9 @@ def kinetic_matrix(
         raise Exception(
             f'No initial concentration specified in dataset "{dataset_descriptor.label}"'
         )
-    initial_concentration = dataset_descriptor.initial_concentration.normalized(dataset_descriptor)
+    initial_concentration = dataset_descriptor.initial_concentration.normalized()
 
-    for k_matrix in k_matrices:
+    for k_matrix_index, k_matrix in enumerate(k_matrices):
 
         if k_matrix is None:
             continue
@@ -46,6 +46,9 @@ def kinetic_matrix(
             matrix_implementation,
         )
 
+        if megacomplex_scales is not None:
+            this_matrix *= megacomplex_scales[k_matrix_index]
+
         if matrix is None:
             compartments = this_compartments
             matrix = this_matrix
@@ -54,11 +57,11 @@ def kinetic_matrix(
                 c for c in this_compartments if c not in compartments
             ]
             new_matrix = np.zeros((matrix.shape[0], len(new_compartments)), dtype=np.float64)
-            for i, comp in enumerate(new_compartments):
+            for idx, comp in enumerate(new_compartments):
                 if comp in compartments:
-                    new_matrix[:, i] += matrix[:, compartments.index(comp)]
+                    new_matrix[:, idx] += matrix[:, compartments.index(comp)]
                 if comp in this_compartments:
-                    new_matrix[:, i] += this_matrix[:, this_compartments.index(comp)]
+                    new_matrix[:, idx] += this_matrix[:, this_compartments.index(comp)]
             compartments = new_compartments
             matrix = new_matrix
 
@@ -129,7 +132,8 @@ def kinetic_image_matrix_implementation(
                 backsweep,
                 backsweep_period,
             )
-        matrix /= np.sum(irf_scale)
+        if dataset_descriptor.irf.normalize:
+            matrix /= np.sum(irf_scale)
 
     else:
         calculate_kinetic_matrix_no_irf(matrix, rates, axis)
diff --git a/glotaran/builtin/models/kinetic_image/kinetic_image_megacomplex.py b/glotaran/builtin/models/kinetic_image/kinetic_image_megacomplex.py
index fdd00154e..0d090cae2 100644
--- a/glotaran/builtin/models/kinetic_image/kinetic_image_megacomplex.py
+++ b/glotaran/builtin/models/kinetic_image/kinetic_image_megacomplex.py
@@ -3,18 +3,19 @@
 from typing import List
 
 from glotaran.model import model_attribute
-from glotaran.parameter import Parameter
 
 
 @model_attribute(
     properties={
         "k_matrix": {"type": List[str], "default": []},
-        "scale": {"type": Parameter, "allow_none": True},
     }
 )
 class KineticImageMegacomplex:
     """A Megacomplex with one or more K-Matrices."""
 
+    def has_k_matrix(self) -> bool:
+        return len(self.k_matrix) != 0
+
     def full_k_matrix(self, model=None):
         full_k_matrix = None
         for k_matrix in self.k_matrix:
diff --git a/glotaran/builtin/models/kinetic_image/kinetic_image_result.py b/glotaran/builtin/models/kinetic_image/kinetic_image_result.py
index eeb523716..887a48a59 100644
--- a/glotaran/builtin/models/kinetic_image/kinetic_image_result.py
+++ b/glotaran/builtin/models/kinetic_image/kinetic_image_result.py
@@ -12,11 +12,12 @@ def finalize_kinetic_image_result(model, problem: Problem, data: dict[str, xr.Da
     for label, dataset in data.items():
 
         dataset_descriptor = problem.filled_dataset_descriptors[label]
-        if not dataset_descriptor.get_k_matrices():
+
+        if not dataset_descriptor.has_k_matrix():
             continue
 
-        retrieve_species_assocatiated_data(problem.model, dataset, dataset_descriptor, "images")
-        retrieve_decay_assocatiated_data(problem.model, dataset, dataset_descriptor, "images")
+        retrieve_species_associated_data(problem.model, dataset, dataset_descriptor, "images")
+        retrieve_decay_associated_data(problem.model, dataset, dataset_descriptor, "images")
 
         if dataset_descriptor.baseline:
             dataset["baseline"] = dataset.clp.sel(clp_label=f"{dataset_descriptor.label}_baseline")
@@ -24,7 +25,7 @@ def finalize_kinetic_image_result(model, problem: Problem, data: dict[str, xr.Da
         retrieve_irf(problem.model, dataset, dataset_descriptor, "images")
 
 
-def retrieve_species_assocatiated_data(model, dataset, dataset_descriptor, name):
+def retrieve_species_associated_data(model, dataset, dataset_descriptor, name):
     compartments = dataset_descriptor.initial_concentration.compartments
 
     compartments = [c for c in compartments if c in dataset_descriptor.compartments()]
@@ -59,7 +60,7 @@ def retrieve_species_assocatiated_data(model, dataset, dataset_descriptor, name)
         )
 
 
-def retrieve_decay_assocatiated_data(model, dataset, dataset_descriptor, name):
+def retrieve_decay_associated_data(model, dataset, dataset_descriptor, name):
     # get_das
     all_das = []
     all_a_matrix = []
diff --git a/glotaran/builtin/models/kinetic_image/test/test_k_matrix.py b/glotaran/builtin/models/kinetic_image/test/test_k_matrix.py
index 128765e97..5ec7d928e 100644
--- a/glotaran/builtin/models/kinetic_image/test/test_k_matrix.py
+++ b/glotaran/builtin/models/kinetic_image/test/test_k_matrix.py
@@ -274,3 +274,29 @@ def test_unibranched():
 
     print(mat.a_matrix_unibranch(con))
     assert np.allclose(mat.a_matrix_unibranch(con), wanted_a_matrix)
+
+
+def test_combine_matrices():
+
+    matrix1 = {
+        ("s1", "s1"): "1",
+        ("s2", "s2"): "2",
+    }
+    mat1 = KMatrix()
+    mat1.label = "A"
+    mat1.matrix = matrix1
+
+    matrix2 = {
+        ("s2", "s2"): "3",
+        ("s3", "s3"): "4",
+    }
+    mat2 = KMatrix()
+    mat2.label = "B"
+    mat2.matrix = matrix2
+
+    combined = mat1.combine(mat2)
+
+    assert combined.label == "A+B"
+    assert combined.matrix[("s1", "s1")].full_label == "1"
+    assert combined.matrix[("s2", "s2")].full_label == "3"
+    assert combined.matrix[("s3", "s3")].full_label == "4"
diff --git a/glotaran/builtin/models/kinetic_spectrum/kinetic_spectrum_result.py b/glotaran/builtin/models/kinetic_spectrum/kinetic_spectrum_result.py
index c70f8fb8b..721eeb6f4 100644
--- a/glotaran/builtin/models/kinetic_spectrum/kinetic_spectrum_result.py
+++ b/glotaran/builtin/models/kinetic_spectrum/kinetic_spectrum_result.py
@@ -5,9 +5,9 @@
 from glotaran.analysis.problem import Problem
 
 from ..kinetic_image.irf import IrfMultiGaussian
-from ..kinetic_image.kinetic_image_result import retrieve_decay_assocatiated_data
+from ..kinetic_image.kinetic_image_result import retrieve_decay_associated_data
 from ..kinetic_image.kinetic_image_result import retrieve_irf
-from ..kinetic_image.kinetic_image_result import retrieve_species_assocatiated_data
+from ..kinetic_image.kinetic_image_result import retrieve_species_associated_data
 from .spectral_irf import IrfGaussianCoherentArtifact
 from .spectral_irf import IrfSpectralMultiGaussian
 
@@ -17,15 +17,15 @@ def finalize_kinetic_spectrum_result(model, problem: Problem, data: dict[str, xr
     for label, dataset in data.items():
 
         dataset_descriptor = problem.filled_dataset_descriptors[label]
-        if not dataset_descriptor.get_k_matrices():
+        if not dataset_descriptor.has_k_matrix():
             continue
 
-        retrieve_species_assocatiated_data(problem.model, dataset, dataset_descriptor, "spectra")
+        retrieve_species_associated_data(problem.model, dataset, dataset_descriptor, "spectra")
 
         if dataset_descriptor.baseline:
             dataset["baseline"] = dataset.clp.sel(clp_label=f"{dataset_descriptor.label}_baseline")
 
-        retrieve_decay_assocatiated_data(problem.model, dataset, dataset_descriptor, "spectra")
+        retrieve_decay_associated_data(problem.model, dataset, dataset_descriptor, "spectra")
 
         irf = dataset_descriptor.irf
         if isinstance(irf, IrfMultiGaussian):
diff --git a/glotaran/model/dataset_descriptor.py b/glotaran/model/dataset_descriptor.py
index 947b89528..fd39c35c7 100644
--- a/glotaran/model/dataset_descriptor.py
+++ b/glotaran/model/dataset_descriptor.py
@@ -10,6 +10,7 @@
 @model_attribute(
     properties={
         "megacomplex": List[str],
+        "megacomplex_scale": {"type": List[Parameter], "default": None, "allow_none": True},
         "scale": {"type": Parameter, "default": None, "allow_none": True},
     }
 )
diff --git a/glotaran/model/test/test_model.py b/glotaran/model/test/test_model.py
index 31fa33dfd..c523c07e2 100644
--- a/glotaran/model/test/test_model.py
+++ b/glotaran/model/test/test_model.py
@@ -75,7 +75,7 @@ def model():
                 "megacomplex": ["m1", "m2"],
                 "scale": "scale_1",
             },
-            "dataset2": [["m2"], "scale_2"],
+            "dataset2": [["m2"], ["bar"], "scale_2"],
         },
     }
     return MockModel.from_dict(d)
@@ -98,7 +98,7 @@ def model_error():
                 "megacomplex": ["N1", "N2"],
                 "scale": "scale_1",
             },
-            "dataset2": [["mrX"], "scale_3"],
+            "dataset2": [["mrX"], ["bar"], "scale_3"],
         },
     }
     return MockModel.from_dict(d)