diff --git a/src/Lasso.jl b/src/Lasso.jl
index a3625d8..df8981a 100644
--- a/src/Lasso.jl
+++ b/src/Lasso.jl
@@ -209,6 +209,10 @@ const MAX_DEV_FRAC = 0.999
 # Compute automatic λ values based on λmax and λminratio
 function computeλ(λmax, λminratio, α, nλ)
     λmax /= α
+    if isapprox(λmax, 0; atol=1e-10)  # then assuming λmax = 0
+        @info "The penalized coefficients equal zero for all values of the regularization parameter λ."
+        return [0]
+    end
     logλmax = log(λmax)
     exp.(range(logλmax, stop=logλmax + log(λminratio), length=nλ))
 end
diff --git a/src/coordinate_descent.jl b/src/coordinate_descent.jl
index f8d71ee..67f69ea 100644
--- a/src/coordinate_descent.jl
+++ b/src/coordinate_descent.jl
@@ -685,7 +685,7 @@ function StatsBase.fit!(path::RegularizationPath{S,T}; verbose::Bool=false, irls
     niter = 0
     if nλ == 0
         i = 0
-    else
+    elseif i <= nλ  # need this check because it is possible that autoλ is true and nλ is 1
         while true # outer loop
             obj = convert(T, Inf)
             last_dev_ratio = dev_ratio
@@ -776,6 +776,7 @@ function StatsBase.fit!(path::RegularizationPath{S,T}; verbose::Bool=false, irls
         end
     end
 
+    i = min(i, nλ)
     path.λ = path.λ[1:i]
     path.pct_dev = pct_dev[1:i]
     path.coefs = coefs[:, 1:i]
@@ -819,29 +820,32 @@ function StatsBase.fit!(path::RegularizationPath{S,T}; verbose::Bool=false,
         i = 1
     end
 
-    while true # outer loop
-        last_dev_ratio = dev_ratio
-        curλ = λ[i]
+    if i <= nλ  # need this check because it is possible that autoλ is true and nλ is 1
+        while true # outer loop
+            last_dev_ratio = dev_ratio
+            curλ = λ[i]
 
-        # Run coordinate descent
-        niter += cdfit!(newcoef, cd, curλ, criterion)
+            # Run coordinate descent
+            niter += cdfit!(newcoef, cd, curλ, criterion)
 
-        dev_ratio = cd.dev/nulldev
-        pct_dev[i] = 1 - dev_ratio
-        addcoefs!(coefs, newcoef, i)
-        b0s[i] = intercept(newcoef, cd)
+            dev_ratio = cd.dev/nulldev
+            pct_dev[i] = 1 - dev_ratio
+            addcoefs!(coefs, newcoef, i)
+            b0s[i] = intercept(newcoef, cd)
 
-        # Test whether we should continue
-        if i == nλ || (stopearly && autoλ && (last_dev_ratio - dev_ratio < MIN_DEV_FRAC_DIFF ||
-                       pct_dev[i] > MAX_DEV_FRAC))
-            break
-        end
+            # Test whether we should continue
+            if i == nλ || (stopearly && autoλ && (last_dev_ratio - dev_ratio < MIN_DEV_FRAC_DIFF ||
+                           pct_dev[i] > MAX_DEV_FRAC))
+                break
+            end
 
-        verbose && println("$i: λ=$curλ, pct_dev=$(pct_dev[i])")
-        poststep(path, cd, i, newcoef)
-        i += 1
+            verbose && println("$i: λ=$curλ, pct_dev=$(pct_dev[i])")
+            poststep(path, cd, i, newcoef)
+            i += 1
+        end
     end
 
+    i = min(i, nλ)
     path.λ = path.λ[1:i]
     path.pct_dev = pct_dev[1:i]
     path.coefs = coefs[:, 1:i]
diff --git a/test/lasso.jl b/test/lasso.jl
index 0b4917b..4f6d7ed 100644
--- a/test/lasso.jl
+++ b/test/lasso.jl
@@ -154,6 +154,24 @@ end
     end
 end
 
+# Test case with zero variation in y is handled correctly
+function zero_variation_test()
+    X = [
+        0.5472502169628388 0.37660447632078875 0.06669114126498532 0.4950818154768257;
+        0.5142931961160688 0.520205941129849 0.4052730635141131 0.6700530909562794;
+        0.5831846867316071 0.3174143498124731 0.772131243876973 0.03386847158881201;
+        0.8802489459954292 0.6742158685234003 0.3849775799923969 0.7773264968613842;
+        0.9216786846192617 0.7888303438159934 0.09788865152005011 0.34950775139369905
+    ]
+    y = 0.2937233091452627 .+ zeros(size(X, 1))
+    path = fit(LassoPath, X, y)
+    (path.λ == eltype(path.λ)[0]) || return false
+    (length(path.coefs.nzval) == 0) || return false
+    return true
+end
+
+@test zero_variation_test() == true
+
 # Test for sparse matrices
 
 # @testset "LassoPath Zero in" begin