diff --git a/source/structured_data.cc b/source/structured_data.cc
index 79bfe2dd0f3..8c88da886c8 100644
--- a/source/structured_data.cc
+++ b/source/structured_data.cc
@@ -327,13 +327,14 @@ namespace aspect
               if (components == numbers::invalid_unsigned_int)
                 components = name_column_index - dim;
               else if (name_column_index != 0)
-                AssertThrow (components == name_column_index,
+                AssertThrow (components+dim == name_column_index,
                              ExcMessage("The number of expected data columns and the "
                                         "list of column names at the beginning of the data file "
                                         + filename + " do not match. The file should contain "
-                                        "one column name per column (one for each dimension "
-                                        "and one per data column)."));
-
+                                        + Utilities::int_to_string(name_column_index) + " column "
+                                        "names (one for each dimension and one per data column), "
+                                        "but it only has " + Utilities::int_to_string(components+dim) +
+                                        " column names."));
               break;
             }
           catch (const boost::bad_lexical_cast &e)
@@ -380,6 +381,29 @@ namespace aspect
             column_names.push_back("column " + Utilities::int_to_string(c,2));
         }
 
+      // Make sure the data file actually has as many columns as we think it has
+      // (either based on the header, or based on what was passed to the reinit function).
+      const unsigned int position = in.tellg();
+      std::string first_data_row;
+      std::getline(in, first_data_row);
+      std::stringstream linestream(first_data_row);
+      std::string column_entry;
+
+      // We have already read in the first data entry above in the try/catch block,
+      // so there's one more column in the file than in the line we just read in.
+      unsigned int number_of_entries = 1;
+      while (linestream >> column_entry)
+        number_of_entries += 1;
+
+      AssertThrow ((number_of_entries) == column_names.size()+dim,
+                   ExcMessage("ERROR: The number of columns in the data file " + filename +
+                              " is incorrect. It needs to have " + Utilities::int_to_string(column_names.size()+dim) +
+                              " columns, but the first row has " + Utilities::int_to_string(number_of_entries) +
+                              " columns."));
+
+      // Go back to the position in the file where we started the check for the column numbers.
+      in.seekg (position);
+
       // Finally read data lines:
       unsigned int read_data_entries = 0;
       do
@@ -396,13 +420,14 @@ namespace aspect
 
               AssertThrow(old_value == 0. ||
                           (std::abs(old_value-temp_data) < 1e-8*std::abs(old_value)),
-                          ExcMessage("Invalid coordinate "
+                          ExcMessage("Invalid coordinate in column "
                                      + Utilities::int_to_string(column_num) + " in row "
                                      + Utilities::int_to_string(row_num)
                                      + " in file " + filename +
                                      "\nThis class expects the coordinates to be structured, meaning "
                                      "the coordinate values in each coordinate direction repeat exactly "
-                                     "each time."));
+                                     "each time. This also means each row in the data file has to have "
+                                     "the same number of columns as the first row containing data."));
 
               coordinate_values[column_num][idx[column_num]] = temp_data;
             }