diff --git a/qt/scientific_interfaces/Indirect/IndirectDataTablePresenter.cpp b/qt/scientific_interfaces/Indirect/IndirectDataTablePresenter.cpp
index ee5d70be53c5..06478a8b7165 100644
--- a/qt/scientific_interfaces/Indirect/IndirectDataTablePresenter.cpp
+++ b/qt/scientific_interfaces/Indirect/IndirectDataTablePresenter.cpp
@@ -136,18 +136,17 @@ QString IndirectDataTablePresenter::getText(FitDomainIndex row,
 
 void IndirectDataTablePresenter::removeSelectedData() {
   auto selectedIndices = m_dataTable->selectionModel()->selectedIndexes();
-
-  for (auto item : selectedIndices) {
-    m_model->removeDataByIndex(FitDomainIndex(item.row()));
+  std::sort(selectedIndices.begin(), selectedIndices.end());
+  for (auto item = selectedIndices.end(); item != selectedIndices.begin();) {
+    --item;
+    m_model->removeDataByIndex(FitDomainIndex(item->row()));
   }
-
   updateTableFromModel();
 }
 
 void IndirectDataTablePresenter::updateTableFromModel() {
   ScopedFalse _signalBlock(m_emitCellChanged);
   m_dataTable->setRowCount(0);
-
   for (auto domainIndex = FitDomainIndex{0};
        domainIndex < m_model->getNumberOfDomains(); domainIndex++) {
     addTableEntry(domainIndex);
diff --git a/qt/scientific_interfaces/Indirect/IndirectFitData.cpp b/qt/scientific_interfaces/Indirect/IndirectFitData.cpp
index a00135a8ddc4..7b74f8e8f03c 100644
--- a/qt/scientific_interfaces/Indirect/IndirectFitData.cpp
+++ b/qt/scientific_interfaces/Indirect/IndirectFitData.cpp
@@ -234,9 +234,11 @@ Spectra &Spectra::operator=(Spectra &&vec) {
   return *this;
 }
 
-bool Spectra::empty() const { return m_vec.empty(); }
+[[nodiscard]] bool Spectra::empty() const { return m_vec.empty(); }
 
-FitDomainIndex Spectra::size() const { return FitDomainIndex{m_vec.size()}; }
+FitDomainIndex Spectra::size() const {
+  return FitDomainIndex{m_vec.size()};
+}
 
 std::string Spectra::getString() const {
   if (empty())
@@ -348,7 +350,7 @@ Mantid::API::MatrixWorkspace_sptr IndirectFitData::workspace() const {
 
 const Spectra &IndirectFitData::spectra() const { return m_spectra; }
 
-Spectra IndirectFitData::getMutableSpectra() { return m_spectra; }
+Spectra &IndirectFitData::getMutableSpectra() { return m_spectra; }
 
 WorkspaceIndex IndirectFitData::getSpectrum(FitDomainIndex index) const {
   return m_spectra[index];
diff --git a/qt/scientific_interfaces/Indirect/IndirectFitData.h b/qt/scientific_interfaces/Indirect/IndirectFitData.h
index 4b5cc7f773c5..53f9985b6438 100644
--- a/qt/scientific_interfaces/Indirect/IndirectFitData.h
+++ b/qt/scientific_interfaces/Indirect/IndirectFitData.h
@@ -120,7 +120,7 @@ class MANTIDQT_INDIRECT_DLL IndirectFitData {
 
   Mantid::API::MatrixWorkspace_sptr workspace() const;
   const Spectra &spectra() const;
-  Spectra getMutableSpectra();
+  Spectra &getMutableSpectra();
   WorkspaceIndex getSpectrum(FitDomainIndex index) const;
   FitDomainIndex numberOfSpectra() const;
   bool zeroSpectra() const;
diff --git a/qt/scientific_interfaces/Indirect/IndirectFitDataModel.cpp b/qt/scientific_interfaces/Indirect/IndirectFitDataModel.cpp
index 1713c524d384..eb3d3a8f0768 100644
--- a/qt/scientific_interfaces/Indirect/IndirectFitDataModel.cpp
+++ b/qt/scientific_interfaces/Indirect/IndirectFitDataModel.cpp
@@ -310,9 +310,13 @@ void IndirectFitDataModel::removeWorkspace(TableDatasetIndex index) {
 
 void IndirectFitDataModel::removeDataByIndex(FitDomainIndex fitDomainIndex) {
   auto subIndices = getSubIndices(fitDomainIndex);
-  m_fittingData->at(subIndices.first.value)
-      .getMutableSpectra()
-      .erase(subIndices.second);
+  auto &spectra = m_fittingData->at(subIndices.first.value).getMutableSpectra();
+  spectra.erase(subIndices.second);
+  // If the spectra list corresponding to a workspace is empty, remove workspace
+  // at this index, else we'll have a workspace persist with no spectra loaded.
+  if (spectra.empty()) {
+    removeWorkspace(subIndices.first.value);
+  }
 }
 
 void IndirectFitDataModel::switchToSingleInputMode() {