diff --git a/R/glm_tools.R b/R/glm_tools.R
index f7b21314..f1b1fac5 100644
--- a/R/glm_tools.R
+++ b/R/glm_tools.R
@@ -53,49 +53,57 @@ fit_glm <- function(target, mm, nb_vals) {
   assertthat::assert_that(nrow(mm) > 0)
   engine <- options()[["mixvlmc.predictive"]]
   assertthat::assert_that(engine %in% c("glm", "multinom"))
-  if (engine == "glm") {
-    if (nb_vals == 2) {
-      if (ncol(mm) > 0) {
-        suppressWarnings(result <-
-          stats::glm(target ~ .,
-            data = mm, family = stats::binomial(),
-            method = spaMM::spaMM_glm.fit, x = FALSE, y = FALSE,
-            model = FALSE
-          ))
+  target_dist <- table(target)
+  target_dist <- target_dist[target_dist > 0]
+  if (length(target_dist) == 1) {
+    ## degenerate case
+    constant_model(target, mm, nb_vals)
+  } else {
+    if (engine == "glm") {
+      if (nb_vals == 2) {
+        if (ncol(mm) > 0) {
+          suppressWarnings(result <-
+            stats::glm(target ~ .,
+              data = mm, family = stats::binomial(),
+              method = spaMM::spaMM_glm.fit, x = FALSE, y = FALSE,
+              model = FALSE
+            ))
+        } else {
+          suppressWarnings(result <-
+            stats::glm(target ~ 1,
+              family = stats::binomial(),
+              method = spaMM::spaMM_glm.fit, x = FALSE, y = FALSE,
+              model = FALSE
+            ))
+        }
       } else {
-        suppressWarnings(result <-
-          stats::glm(target ~ 1,
-            family = stats::binomial(),
-            method = spaMM::spaMM_glm.fit, x = FALSE, y = FALSE,
-            model = FALSE
-          ))
+        if (ncol(mm) > 0) {
+          suppressWarnings(result <-
+            VGAM::vglm(target ~ .,
+              data = mm, family = VGAM::multinomial(),
+              x.arg = FALSE, y.arg = FALSE, model = FALSE
+            ))
+        } else {
+          suppressWarnings(result <-
+            VGAM::vglm(target ~ 1,
+              data = mm, family = VGAM::multinomial(),
+              x.arg = FALSE, y.arg = FALSE, model = FALSE
+            ))
+        }
       }
-    } else {
+      result
+    } else if (engine == "multinom") {
       if (ncol(mm) > 0) {
-        suppressWarnings(result <-
-          VGAM::vglm(target ~ .,
-            data = mm, family = VGAM::multinomial(),
-            x.arg = FALSE, y.arg = FALSE, model = FALSE
-          ))
+        result <- nnet::multinom(target ~ ., data = mm, trace = FALSE)
       } else {
-        suppressWarnings(result <-
-          VGAM::vglm(target ~ 1,
-            data = mm, family = VGAM::multinomial(),
-            x.arg = FALSE, y.arg = FALSE, model = FALSE
-          ))
+        result <- nnet::multinom(target ~ 1, trace = FALSE)
       }
-    }
-    result
-  } else if (engine == "multinom") {
-    if (ncol(mm) > 0) {
-      result <- nnet::multinom(target ~ ., data = mm, trace = FALSE)
+      result$rank <- length(result$wts)
+      result
     } else {
-      result <- nnet::multinom(target ~ 1, trace = FALSE)
+      ## should not happen
+      NULL
     }
-    result$rank <- length(result$wts)
-    result
-  } else {
-    NULL
   }
 }